String Theory and M-Theory: A Modern Introduction
Average customer rating: 4.5 out of 5 stars
  • A good general introduction
  • Excellent Book
  • Best of All Worlds
  • A Modern Fairytale
  • Most up-to-date string theory tome published this year.
String Theory and M-Theory: A Modern Introduction
Katrin Becker , Melanie Becker , and John H. Schwarz
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521860695

Book Description

String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697.

Customer Reviews:

4 out of 5 stars A good general introduction.......2007-04-22

String theory has been criticized since it was first invented but not to the degree that it has now, this criticism mostly focusing on its failure to connect with observation. The criticism has increased dramatically in recent years however, and some of this has been too vituperative to be useful to those curious about string theory as a viable physical theory. But criticism, however harsh, can be healthy, since it motivates the proponents of a theory to more carefully elucidate its foundations and content. This is usually not the case when a theory is popular, as researchers are in a competitive spirit and are hesitant to share the knowledge to possible competitors. At this stage in the game however, string theorists it seems are now on the defensive, and have thus taken the time to discuss in-depth what this reviewer still believes is the most complex and beautiful theory ever constructed in mathematical physics. String theory still has a long way to go before it gains status as being a physical theory, but hopefully by the end of the next few decades one will see the appearance of charts, graphs, and numerical calculations in books on string theory, much like one finds in the most successful of all physical theories to date: relativistic quantum field theory.
Some highlights in the book that are particularly insightful include:
1. The observation that Dirichlet boundary conditions (for the open string) break Poincare invariance, but that this leads to the introduction of Dp-branes as positions of the endpoints of the open string. Poincare invariance is recovered as long as Dp-brane is space filling, i.e. has a dimension one less than the background spacetime.
2. The view that the BRST quantization of the path integral is really a conformal field theory. This is interesting in that BRST analysis is typically thought of as a procedure for quantizing constrained systems (gauge theories being predominant examples).
3. The `Myers effect'. Sometimes referred to as the `D-brane dielectric effect', it is part of an attempt to understand the physics of non-Abelian D-branes for strong fields. One of the challenges in this understanding involves the validity of the Dirac-Born-Infeld action in these kinds of circumstances, which as the authors remark is designed for situations where the background fields and world-volume gauge fields do not vary appreciably over the distances on the order of the string scale.
4. The origin of the (classical) Virasoro algebra as the freedom of choice of gauge in the reparametrization symmetry. And along these same lines, the quantization of the Virasoro algebra is defined to the normal ordering of the Virasoro generators, and their commutators give an expression consisting of the ordinary classical term plus a "quantum" correction, the famous central extension. Thus the quantum Virasoro algebra can be viewed as a "quantum deformation" of the classical Virasoro algebra, with the central parameter as being the deformation parameter. This philosophy of deformation has found generalization in what are now called `quantum groups' (even though strictly speaking they are much more complicated objects than ordinary groups).
5. The connection of the dilaton to the Euler characteristic.
6. The role of the GSO projection in insuring consistency in the state spectrum.
7. The use of (vector bundle) K-theory to classify D-brane charges. This use arises when it is realized that the conserved R-R charges cannot be identified with cohomology classes of gauge field configurations. Instead, the D-branes are classified by K-theory classes.
8. The discussion on `primitive cohomology' and its relation to de Rham cohomology and Hodge theory.
9. The role of the Born-Infeld structure in ensuring Lorentz invariance of the T-dual description. The Born-Infeld action was once viewed as a mere historical curiosity, namely as a nonlinear generalization of the Maxwell theory, with no experimental backing. That it finds such a natural place in string theory is very interesting (but still of course lacking in experimental support).
10. The derivation of a lower bound for Newton's constant from heterotic M-theory, which is close to the observed value.
11. The argument, beautifully elucidated in this book, that type IIA supergravity may be obtained from 11-dimensional supergravity by dimensional reduction.
12. The discussion on warped space-times and the gauge hierarchy. The authors cleverly motivate this subject by asking why Newtonian gravity follows an inverse-square law rather than an inverse-cube law.
13. An entire chapter is devoted to "stringy" geometry, which is a fascinating subject given that it touches so many areas of modern mathematics.
14. The discussion of the `hidden sector' and its conjectured relation to dark matter and supersymmetry breaking.
15. The author's treatment of the AdS/CFT conjecture is superb and is by far the most interesting part of the book. The dualities shown to exists between gauge theory and string theory are a possible route to a full understanding of nonperturbative quantum chromodynamics, which to this date has defied resolution.

Some major omissions or discussions that need more elaboration include:
1. The difficulties that are actually involved in quantizing the Nambu-Goto action. The authors remark that this is due to the presence of the square root, but it would have been interesting if they would have indicated just where the trouble rises explicitly when a quantization procedure is attempted with the Nambu-Goto action. In ordinary quantum field theory, the presence of the square root is interpreted as a "nonlocal" problem, but even there this issue is not usually dealt with in a manner that is very transparent.
2. A more detailed treatment of string field theory for those readers who want to compare it to what is done in second quantization in ordinary quantum field theory.
3. The role of the Beltrami differentials in the attaining of a measure for moduli space that is invariant under reparametrizations of the moduli space.
4. No in-depth discussion of characteristic classes over and above the algebra involved in their manipulation (i.e. the wedge products). An understanding of characteristic classes is crucial to understanding superstring and brane theory, but the pages of this book mislead the unsuspecting reader that there is nothing to characteristic classes except algebraic manipulation of the differential forms. But characteristic classes have a deep geometrical meaning, and obtaining insight into this meaning has been proven to be difficult for students of string theory. This book does not provide any of this insight, nor do any of the other books currently in print on string theory.
5. Is supersymmetry absolutely necessary for the incorporation of fermions into string theory? The authors seem to argue that it is, but an explicit proof is lacking.
6. The proof that `threshold bound states' are stable is omitted, disappointing the more mathematically sophisticated reader. As the authors remark, the proof involves a special type of index theory involving non-Fredholm operators, and where one must deal with a continuous spectrum. The usual index theory breaks down since one is only dealing with elliptic operators, and contributions to the index from bosons and fermions do not necessarily have to be integers.
7. The authors should have included more discussion on mirror symmetry, beautiful subject that it is.
8. Dp-branes are asserted to be useful in incorporating non-Abelian gauge symmetries in string theory, in that they appear "naturally" as confined to world volumes of multiply-coincident Dp-branes. But is this the best way to introduce these symmetries? Is there a method, other than this one and `compactification', that is just as "natural" and does not have the contrived element that the introduction of Dp-branes sometimes has?
9. The authors need to elaborate in more detail on the definition of "stable" and "unstable" D-brane.
10. The omitting of the proof that string theories are ultraviolet finite theories of quantum gravity. This is by far the most serious omission in the book. This reviewer does not know of a reference that proves this assertion, and many in the physics community have pointed to this omission as being a sign that the string theory research community has been misled by false assertions of proof.

5 out of 5 stars Excellent Book.......2007-03-11

I think this is a great book that provides not only a great introduction to string theory (there is no assumed prior knowledge of string theory), but also provides coverage of many more advanced topics as well. I think it's likely that the vast majority of students specializing in string theory will want to read it at some point in their studies.

The coverage of topics in the first few chapters is in some ways fairly standard. The first two chapters consists of a high level overview of string theory, bosonic string, the Nambu-Goto action the Polyakov action, the Virasoro algebra, the critical dimension, light code gauge and the spectra of open/closed strings. After this there is a chapter on conformal field theory, naturally emphasizing the parts relevant to string theory (including a bit of string field theory). This is followed by discussions of worldsheet supersymmetry, spacetime supersymmetry, anomalies, T-duality and heterotic strings. The writing is very clear and considering the nature of the material, fairly straight forward. There are two things that I considered exceptional strengths. One is that the discussions incorporate D-branes, M-theory and the (unexpected) symmetries of string theory early on. The other is that there are numerous worked examples, as there are throughout the book.

At a very high level the rest of the book contains more extensive discussions of M-theory, compactification (including a substantial amount besides the standard approach of the compact dimensions being a Calabi-Yau space), mirror symmetry, S-duality, possible cosmological consequences of string theory, black holes and other solutions with horizons, matrix theory, AdS/CFT correspondence (a proposed equivalence between closed string solutions on the product of a sphere and anti-deSitter space and Yang-Mills theories) and the holographic principle (or as some would say conjecture).

The things I appreciated the most about this material was that is was a very interesting mix of topics. The discussion of black holes and cosmology was fairly extensive (for cosmology it was the most extensive I've seen in a text book). As was the coverage of the AdS/CFT correspondence. There were also some topics that I don't recall seeing in other string theory books, such as warped geometries in compactification and S-branes (these are like D-branes but they satisfy Dirichlet boundary conditions in timelike directions).

Needless to say it's a fairly advanced book. There is some coverage of things like complex spaces, topology, general relativity and cosmology. However this material is more along the lines of a review, not something intended to teach from first principles (some of the other string theory books cover this kind material in more detail).

All-in-all I believe this book not only provides a great introduction, it also provides an excellent treatment of some of the more advanced topics in string theory.

4 out of 5 stars Best of All Worlds.......2007-03-09

This new textbook on string theory might be considered a modern pimped up version of Zwiebach's introductory course. The book is - as an introduction - better than the 2-volume set by Schwarz (Green, Schwarz, Witten), which is partly outdated, and on the same footing as Polchinski's version, but certainly not as thorough and elaborate. There is some overlap between all books (e.g. the CFT bits from Polchinski are quite similar to those in this new text, the introduction of the bosonic string via the relativistic point particle looks like the ones by Polchinski and Zwiebach, but Becker & Schwarz immediately generalise the concept to p-branes, SCFTs are discussed in a similar manner as in Polchinski, and so on), but there are additional features that really add to the value of the book: all exercises within the text have solutions directly under them, so one can either try to solve them or read them through, and some parts are explained more clearly. The concepts of "(gauge) symmetries" are discussed slightly better than by Polchsinki or GSW, but for those who want mathematical proofs instead of hand-waving arguments, and more background material on supersymmetry, I can only say that I have found no books on string theory that really do that. Both are subjects of study on their own and would go "beyond the scope" of these books... Nevertheless, a very good introduction and most of all: up to date!

For mid-undergraduates, I think, the perfect sequence for string theory would be (provided one acquires knowledge of QFT and Lie algebras for the more advanced texts):

Zwiebach>Becker/Schwarz>Polchinski (supplemented by GSW's first volume)

But if you want to learn string theory more quickly or if you don't have problems with the very basics, then leave out Zwiebach and go for this one immediately. For graduates, Polchinski should be the start, but one can take Backer/Schwarz always as a references and supplement on some topics (connection to black holes and gauge theories).

5 out of 5 stars A Modern Fairytale.......2007-01-30

This is a fabulous excursion into a world inhabited by all sorts of mythical creatures: Calabi-Yau 3-folds, D-branes, orbifolds, ten and eleven-dimensional backgrounds, supersymmetric partners, covariant fermionic vertex operators and many others that only the wildest imaginations can conceive of. The wizards and magicians who have conjured these beasts have also cast a powerful spell on their easily-beguiled followers who see streets of gold and emerald trees as they walk through the morass of E8*E8 gauge fields, compactifications and dualities. This tome will be a welcome addition to your bookshelf right between Harry Potter and Alice in Wonderland. I gladly recommend each of you to take a brief stroll into this enchanted land to be followed by the volumes of Landau and Lifchitz, so that you will be able to find your way back to reality again. Some have called strings "a theory of anything". Indeed, it is a wonderful place where you can make all your wishes come true. But do not stay too long in the kingdom of string theory lest you end up like so many others who are lost, searching endlessly for the legendary realms of M-theory or wandering aimlessly in the infinite labyrinth of the Landscape, wasting the remaining years of their life on naught but a fable.

4 out of 5 stars Most up-to-date string theory tome published this year........2007-01-24

This volume was authored by one of the most respected researchers in the field, as well as the Becker sisters. It is beautifully illustrated, and is well timed for upcomming experimental tests of superstring theory at the Large Hadron collider. I did not give if five starts because it only devoted four pages to the Landscape, which professor Susskind, the father of string theory, has declared the most significant advance in physics in the past century.
Physics of Sound, The (3rd Edition)
Average customer rating: 4 out of 5 stars
  • Class didnt reflect his own textbook.
  • not helpful
  • Considerably out of date in some places
  • counterbalance to the "bites my..." review
  • This is the Book if You want to Know the"Whats" of Sound!
Physics of Sound, The (3rd Edition)
Richard E Berg , and David G Stork
Manufacturer: Benjamin Cummings
ProductGroup: Book
Binding: Hardcover

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ASIN: 0131457896

Book Description

This book incorporates the developments in digital audio technology, including consumer products, into a firm foundation of the physics of sound. No knowledge of physics, mathematics, or music is required. Includes updated information on musical synthesizers. Provides recent information on the ear, including new advances in cochlear implant technology. Updates material for modern technology, particularly MP3. Features abundant examples, including discussion of demonstration experiments. Includes historical discussion of musical temperaments and instruments. Offers videotapes of musical demonstrations on topics discussed in the book, available from author. A useful reference for musicians or anyone interested in learning more about the physics of music.

Customer Reviews:

3 out of 5 stars Class didnt reflect his own textbook........2007-03-29

Whats better than taking a course where the professor actually wrote the book. Well I did just that and was disappointed. The class had many visual demonstrations but the book had very few pictures which made me wonder why his teaching style did not reflect the textbook.

2 out of 5 stars not helpful.......2006-05-17

Did they even have an editor for this book? I took a class with Dr.Berg and his class was interesting but the book was not helpful nor was it well organized.

3 out of 5 stars Considerably out of date in some places.......2003-12-21

Acoustics is an interesting subject, at all levels, and very important of course due to the human love for music and the need for high fidelity sound reproduction. This book is written for a readership that does not have expertise in physics or mathematics beyond the high school level. The authors do an excellent job, and the book could be used in classes on music theory or a class in physics for the humanities. The audiophile reader will gain a greater appreciation of the physics behind quality sound reproduction. Heavy use is made of demonstrations to illustrate the properties of sound, and most of these are easily set up in the classroom. I have used most of these demonstrations in the classroom, and can highly recommend their use to reinforce the understanding of the physics of sound.

The book opens, appropriately, with a discussion of simple harmonic motion, with the properties of this type of motion related to sound waves. The nature of simple harmonic motion as periodic, in contrast with noise, which is nonperiodic, is pointed out very early on. To introduce the concept of resonance, in particular the concept of coupling resonance, the author use the coupled pendulum system. This demonstration is easily constructed for classroom use and very effective in illustrating coupled resonance. Lissajous figures, which arise in the study of the relationship between two waves, is discussed in some detail.

The difference between longitudinal waves, which sound waves are, and transverse waves (such as light), is illustrated in chapter 2. To reinforce the difference between sound and light, the authors use the "bell in vacuum" demonstration. A demonstration for measuring the speed of sound is also described. Ripple tanks are used to demonstrate Huygen's principle, interference, and parabolic reflectors. The origin of beats, so important in music theory, is discussed, along with a very detailed overview of the Doppler effect. Ultrasound, very important medically, is treated also. A very brief discussion of infrasonic waves is given. Infrasonic waves, which are outside the range of hearing since they are below 20 Hz, are only experienced as vibrations. They have recently been discussed in the popular press as being explanations behind "haunted" houses. The anxiety felt in some old houses is thought of as being due to infrasonic waves.

The origin of the overtone series, so very important in music theory, is discussed in chapter 3. The three laws of Mersenne, which govern the fundamental frequency of stretched wires, are also treated. The Kundt's tube demonstration is used to describe the properties of longitudinal standing waves, and the famous Chladni plates are used to demonstrate standing waves in two dimensions. All throughout the chapter the properties of standing waves are related to music and musical instruments.

Fourier analysis and synthesis, which is typically very formidable mathematically, is presented in chapter 4 in a manner that is very understandable to the targeted readership. The Fourier synthesis of triangular, square, and sawtooth waves, along with a pulse train, is discussed. After a treatment of Fourier spectrum of these waves, the authors discuss the factors contributing to tone quality.

In chapter 5, the authors turn to more practical considerations, wherein they discuss how to create electronic music. Analog synthesizers, although very antiquated by modern standards, are used to illustrate how to combine waves to obtain special sounds or effects. The authors then immediately turn to digital synthesizers and keyboards. They discuss the Musical Instrument Digital Interface (MIDI), but the equipment they illustrate in the chapter is considerably out of date.

The anatomy and physics of the human ear and voice tract are discussed in chapter 6. The diagrams they include are useful, and they discuss the "place theory of hearing" , which is based on the correlation of sound frequency with position of response along the basilar membrane. The critical band, just noticeable difference, and the limit of frequency discrimination are all discussed in the context of this theory, with several different experiments proposed to illustrate these concepts. Most interesting is the discussion on periodicity pitch, which musicians seem to have a knack for. Also interesting is the treatment of vocal formants, which are frequency regions in which harmonics have large amplitudes. Due to the element of subjectivity in hearing and listening, the connection of the material in this chapter to "psychophysics" and "psychoacoustics" is readily apparent.

Most of the next chapter is out-dated since the authors discuss sound reproduction using LPs and tape recorders. However, the authors do discuss how this is done using compact disks, which though are themselves on their way out, due to the rise of the Internet, MP3 formats, and digital music files. Chapter 8 is timeless though, as the authors discuss the acoustics of auditoriums and rooms, detailing the most important acoustical characteristics that contribute to a pleasant musical experience, and some of the problems that arise in acoustical design. The last section of the chapter gives a fairly good overview of what is involved in setting up a home listening room.

In chapter 9, the authors take the plunge into music theory, discussing temperament and musical pitch. The history behind these concepts is detailed, emphasizing in particular that an ideal temperament is not available, its choice being dictated by the musical requirements at hand. Arithmetic descriptions of the Pythagorean, just, mean-tone, Werckmeister, and equal temperaments are given.

The last five chapters are specialized to the principles behind woodwind, brass, string, and percussion instruments, and the piano. The discussion is purely descriptive, but some of the physical principles studied in the first chapters of the book are applied here to give an understanding of the acoustical and musical properties of these instruments.

5 out of 5 stars counterbalance to the "bites my..." review.......2002-02-02

Haven't read the book, but Mr. "bites my wacker" shouldn't be allowed to lower the average score.

5 out of 5 stars This is the Book if You want to Know the"Whats" of Sound!.......1999-04-09

The Physics of Sound is a great book for both musicians and nonmuscians alike. Its not a book for anyone who is afraid of a little mind work. I recommend Physics of Sound because immediately upon after reading it I gained a whole new perspective and deep appreciation for the fundamental elements,and principles that govern this wonderful phenomena we call "SOUND".

Ever wondered how fast sound travel? What about how various sound frequencies react to each other,and in rooms? What exactly is sound? All these questions and more,are answered here. Physics of sound even gives you basic formulas that allow you to manipulate sound in the real world.

Gain Knowledge,Gain Insight,Gain information.
An Introduction to Quantum Field Theory (Frontiers in Physics)
Average customer rating: 3.5 out of 5 stars
  • Perfect.
  • Wow, does this suck . . . get a different book!
  • This book is a very very very bad book which you never buy.
  • Don't make the same fault I did!
  • It is sad that we don't have a better book out there...
An Introduction to Quantum Field Theory (Frontiers in Physics)
Michael E. Peskin , and Dan V. Schroeder
Manufacturer: HarperCollins Publishers
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Binding: Hardcover

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ASIN: 0201503972

Customer Reviews:

5 out of 5 stars Perfect........2007-08-10

I received the book as it should be: knew. And it cames before the estimated time.

1 out of 5 stars Wow, does this suck . . . get a different book!.......2007-06-13

Ok--I just need to help lower the overall rating for this book. I think the people who love it are professors and students who already are familiar with QFT--because it glosses over everything, does pertinent examples, etc. But that's just it, it GLOSSES over everything. Note that nearly all the higher reviews say things like: "oh, you wouldn't want to start with this book." or "Everyone knows that you're going to need more books than this one to understand it . . ." I couldn't even figure out how to create a Feynmann diagram from this book, let alone what one MEANT. FYI, my favorite QFT book so far is Weinberg's Quantum Theory of Fields.

1 out of 5 stars This book is a very very very bad book which you never buy........2007-01-20

Absolutely no logic.
Perfectly nonclear.
No subject.
Mathematically poor.(very poor.)
Nonneccessary words.
No depth.
Not for self-study.
Just arrangement.
No physical insight.
No process.
No thinking.

This is indeed not a book.
This is a stuff for a vanity.
I wonder whether Peskin and Schroeder are genuine physicists.

1 out of 5 stars Don't make the same fault I did!.......2006-12-16

Hi there!

The important information first: I'm a graduate student, mainly interested in theoretical physics. At the moment, I'm trying to get a deeper understanding of QFT.

Peskin's QFT book is NOT the one you should buy if you want to UNDERSTAND renormalization.

I learned the basics of QFT (\phi^4 and QED up to a first contact with renormalization - "trivial" subtraction of infinities) in a lecture and I finally felt like: "What does renormalization mean? What is it good for? Is there a deeper truth in it?" Well, the answer to the last question is definitely yes. It's about the Beta function. This function tells you how the coupling constants of a QFT behave at different momenta. E.g., we can learn from it why perturbation theory works for QED at low energies and for QCD at high energies (I think, this is amazing).

What I just said I learned from Huang's book. Peskin "deals" with it in chapters 10 to 12. In the middle of chapter 12 I finally said to myself: "Hey, don't feel stupid. This book is just completely incomprehensible here."

In my opinion, if you want to see behind renormalization (and therefore behind any QFT(!!)), don't buy Peskin's book. Any other book is better regarding this issue.

3 out of 5 stars It is sad that we don't have a better book out there..........2006-05-28

The main problem of this book: what exactly is it supposed to be?

If it is an introduction, then the opening chapters are written at a level too sophisticated that an average first-time student can't handle.

If it aims to be a "bible" of the subject, then the later chapters are far too technical, loaded with only Feynman diagram calculations for standard model. Not being a phenomenologist, I personally have very little interest in all the technical detail, and apparently several other reviewers share my view here.

Now let me gives some examples to support my claim.

First, C, P and T symmetries are introduced very early on (right after Dirac spinor), and in a very formal way. Yes, they logically belong there, but in an "introduction" of the subject you don't throw out an isolated topic like this which you don't make use of in the following few hundred pages.

The part on cannonical quantization is written at a very fast pace. A complex scalar field is probably the first model you can construct with charged particles. And guess what kind of treatment it receives in this book? Not a single word in the main text. The problem 2 of that chapter essentially asks you to work out the content of this model with few hints given. If you have troble working it out, which is not uncommon for a first-timer, then you won't see the logic behind the decomposition of a complex Dirac field either. This is done in the following chapter, with no explaination.

Like the charged scalar field example, some important pieces of knowledge are hidden only in the exercises. So if you treat these high-power opening chapters as your bible-type reference, you will often end up in the frustrating situation that the book tells you to work out by yourself what you are seeking in the first place.

Now get to the later parts of the book. As I mentioned above, the second half of the book is almost conceptually too simple, overloaded with technical details.

This downfall begins around the renormalization group. On the back of this book, this Prof. Micheal Dine is qouted: "it is the only field theory text with a thoroughly modern, Wilsonian treatment of renormalization". The connection between the Wilsonian idea and dimensional regularization/renormalization scale is shaky at best. You read the text, and are left puzzled at the magic: how does a cut-off scale become some (much lower) arbitrary momentum scale? No explaination. The Wilsonian theory is completely isolated and have little connection with the rest of the renormalization section.

Furthermore, the book does not do a very good job on Lie algebra and non-abilien Lie groups. I mean, come on, if this is an "introduction" type of book, make it more readable. If this is a "bible" type of book, make it more comprehensive.

Having voiced all my bad opinions, I have to admit that the book has its merit. Bottom line is, this is a book written by phenomenologists for phenomenologists. If you view it from such an angle, it is not too badly written after all, and does cover most of the important topics a phnomenologist would want to know. But you may want to start from a more accessible text such as Ryder.

If you are a theorist, but not a phenomenologist, then, well, let's say the ability of getting through the first part perfectly is the minimum requirement for your research.

If you are an experimentalist, don't bother.
Field and Wave Electromagnetics (2nd Edition)
Average customer rating: 4.5 out of 5 stars
  • Second will be better
  • Seeing God (not the author, the creator of the world)
  • Ugh...
  • Excellent Text
  • publisher info is wrong
Field and Wave Electromagnetics (2nd Edition)
David K. Cheng
Manufacturer: Addison-Wesley
ProductGroup: Book
Binding: Hardcover

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  1. Signals and Systems (2nd Edition) Signals and Systems (2nd Edition)
  2. Schaum's Outline of  Electromagnetics Schaum's Outline of Electromagnetics
  3. Microelectronic Circuits: includes CD-ROM (The Oxford Series in Electrical and Computer Engineering) Microelectronic Circuits: includes CD-ROM (The Oxford Series in Electrical and Computer Engineering)
  4. Electromagnetics Problem Solver (Problem Solvers) Electromagnetics Problem Solver (Problem Solvers)
  5. Solid State Electronic Devices (6th Edition) (Prentice Hall Series in Solid State Physical Electronics) Solid State Electronic Devices (6th Edition) (Prentice Hall Series in Solid State Physical Electronics)

ASIN: 0201128195

Customer Reviews:

4 out of 5 stars Second will be better.......2007-04-29

This is the textbook for my sophomore electromagnetics in the electrical engineering. I have to admit I really hated this class then. One is that there are equations here and there and it usually clouds the issue. Another reason is that the author uses the deduction method to describe this topic. It is quite different from the traditional way which goes following the historical developments.

For some reasons, I need to refresh electromagnetics in later years. I re-studied this book and then found it written pretty well this time. It is well-organized and systematic. One weak spot is the explanation for physics. I think it should be made better so that it is easier for readers to absorb the knowledge instead of confused by those mathematical equations.

This book is rather classic, which means it stays at the balance of electromagnetic statics and dynamics. Many recent electromagnetic textbooks are more focused on electromagnetic waves at the expense of the electromagnetic statics. I don't think this is a wise decision since electromagnetic statics is still very important in the real world applications, for example RF IC design.

This book is published almost 20 years ago. But don't regard it as out of date. Based on my acamedic and industrial experience, it is still the best engineering electromagnetic textbook for undergraduates.

5 out of 5 stars Seeing God (not the author, the creator of the world).......2006-12-29

You will finally understand what light is - 10 years after you take the course.

Yes, 2 years after you take the course, you get to arrange waves that can go easily back and forth from wave equations(insane vector calculus) to circuit equations(simple V=IR).

Yes, combined with clever Fourier math, you get to calculate impedance as vector reflection waves, so that you see (through Smith-Chart night vision like mental glasses) the waves invisible to human eyes (but visible to some animals) and make them oscillate/up-down-mix as an EE engineer making a living.

But James Maxwell's math is the only thing interesting in the world, which the book says that well. God made the waves and nothing more. If you want to make stories out of the context or take words out of the context (many books try and do), you give yourself trouble. Yes, we give ourselves troubles all our life. And you will see that in this book. This is life.

Everyone in this world needs to understand how a wave of light is made.

2 out of 5 stars Ugh..........2006-05-11

This book was horrid. I was bombing the class all year with this text, until I bought REA's electromagnetics problem solver. Going into the final, I had maybe a B. By studying the REA book and working my [...] off before the final, I got that up to a final mark of A-. The physics students at my school used Griffith's electrmagnetics book, and they seemed to enjoy that book a lot more.

This book was slightly better when I took a waveguides course... imagine my disgust when I found out we were using this book, again! Even the waveguides sections were still quite weak, though, but they do keep me from rating this book a 1.

5 out of 5 stars Excellent Text.......2006-04-11

While I took Electromagnetic Fields I & II courses using the first and last half of this text, I also purchased other solutions manuals and texts to survive. This was, to me, by far the most clearly written and well-presented text.
16 years after having taken the course, I'm doing a cover-to-cover review of this book and given my industry experience I appreciate the excellence of this book even more. The downside to using it is that I've found a real difficulty in locating the Solutions Manual, leaving me to use others where there's always changes in variables, ordering, and approaches which build in inefficiencies/overhead.

4 out of 5 stars publisher info is wrong.......2006-03-08

The publisher should be "Addison-Wesley," not "Prentice Hall" as shown in amazon.com page.
How to Solve Physics Problems (College Course)
Average customer rating: 4 out of 5 stars
  • Buy this book as a supplement to your textbook
  • Decent book - many errors
  • typographical errors
  • Very helpful, recommend
  • This Is The Book If You Need Help with Physics
How to Solve Physics Problems (College Course)
Robert Oman , and Daniel Oman
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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  1. 3,000 Solved Problems in Physics (Schaum's Solved Problems) (Schaum's Solved Problems Series) 3,000 Solved Problems in Physics (Schaum's Solved Problems) (Schaum's Solved Problems Series)
  2. Physics Problem Solver (Problem Solvers) Physics Problem Solver (Problem Solvers)
  3. Basic Physics: A Self-Teaching Guide (Wiley Self-Teaching Guides) Basic Physics: A Self-Teaching Guide (Wiley Self-Teaching Guides)
  4. Schaum's Outline of College Physics, 10th edition (Schaum's Outlines) Schaum's Outline of College Physics, 10th edition (Schaum's Outlines)
  5. Physics for the Utterly Confused Physics for the Utterly Confused

ASIN: 0070481660

Book Description

275,000 students in noncalculus physics; Required pre-med course; Super-accessible, straightforward help; Student-grabbing graphics and style; Icons for important concepts; 1-2-3 help with problems.

Customer Reviews:

4 out of 5 stars Buy this book as a supplement to your textbook.......2004-07-23

Other than a few typos, this book is awesome. I learn the basic concepts from this book, and then do the problems in my textbook. This book has helped me when my professor couldn't/wouldn't. You cannot learn physics from this book only, but it is an excellent addition to any textbook.

3 out of 5 stars Decent book - many errors.......2000-07-06

This book is a decent book for those being taking a freshman physics course for non-majors. This is a good supplement to a calculus based physics textbook.

4 out of 5 stars typographical errors.......2000-03-08

it's a good book, it helped a great deal. I wish time was taken to correct typographical errors. I lost valuable time that could have been used to study.

5 out of 5 stars Very helpful, recommend.......2000-01-17

this is a very good book except there are some mistakes(but the mistakes are easily found and corrected by yourself). This book gives you how to attack problems in a very organized manner even though the problems are not so difficult. I came to be able to solve more challenging problems in a different book after solving the easy but organized ones in this book. I recommend this book!

5 out of 5 stars This Is The Book If You Need Help with Physics.......2000-01-17

Beginning with the "How To Use This Book" and "How To Excel in Your Physics Course", (especially the latter) and throughout its pages, this is, without a doubt in this readers opinion, the very best book on the subject I have found to date (And I have many). It puts you through the paces. If you want to know this subject and excel in it, these authors have placed before you the practice you will need. I recommend this book highly for your first experiences in this subject. Starting with the mathematical background required; then on to Classical through Special Relativity. It covers each and every topic, in a clear, concise method that enhances learning and improves retention greatly in each and every area. It's a great reference to have on the shelf. EXCELLENT! My thanks to the authors. Your book has helped me much more than I ever expected.
Contemporary College Physics, Third Edition, 2001 Update w/ updated CD-ROM
Average customer rating: 3.5 out of 5 stars
  • a great book for those new to physics
  • A Contemporary Review of "Contemporary College Physics"
  • This is an answer book only! This is not the textbook!
Contemporary College Physics, Third Edition, 2001 Update w/ updated CD-ROM
Edwin R Jones , and Richard L. Childers
Manufacturer: McGraw-Hill Science/Engineering/Math
ProductGroup: Book
Binding: Hardcover

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ASIN: 0072415126

Book Description

This Update of Jones/Childers, CONTEMPORARY COLLEGE PHYSICS, Third Edition adds new biomedical applications and improved technology to the copyright 1999 third edition. Since all exercises from the 1999 edition are retained, the 1999 print supplements will work for the 2001 Update. Jones/Childers 3/e features a strong emphasis on problem solving and a tutorial CD-ROM with multimedia and practice quizzes; the 2001 updates adds more biomedical applications and improves the CD and Website.

Customer Reviews:

4 out of 5 stars a great book for those new to physics.......2002-09-29

As a college student, I always hoped for easy-to-understand textbooks every semester. This book met my expectations! It is taught from a non-calculus point of view...but those of us that know calculus will know how to deal with the myriad of equations that you encounter in physics.

Jones and Childers have put a great textbook together. The chapters are very easy to understand--concepts are explained thoroughly, and then supplemented with examples that are solved step by step and the results are discussed. The figures are drawn well--even things like relativity and quantum mechanics make more sense after reading this book!

To summarize--if this is the textbook for your class, you are in luck. Buy it...if you are interested in physics at all, you will enjoy the book. If you are looking for a book to help learn concepts in physics, and want a textbook, this one is for you too! Compared to all the other textbooks out there, this is one of the top two (Serway's book being the other).

5 out of 5 stars A Contemporary Review of "Contemporary College Physics".......2001-11-03

This book is very well written, due to the choices of sentences and words. The sentences are to the point and not like MANY physics books who dance around the topic. In addition to having carefully chosen examples that illustrates its point clearly.
The book also has nice illustrations printed on nice paper, unlike other EXPENSIVE books printed on "cheap" paper. The book includes all the topics other books would cover in two volumes and hence would cost significantly more. I highly recommend this text for anyone (including poor students like me)!! ;)

1 out of 5 stars This is an answer book only! This is not the textbook!.......1999-10-03

This book is advertised as something it is not. Do not order this book if you want the textbook! This book offers answers to the questions in the text ONLY!
Quantum Field Theory: From Operators to Path Integrals
Average customer rating: 5 out of 5 stars
  • Extremely solid for self-teaching
  • A good introduction to the physics behind renormalization
Quantum Field Theory: From Operators to Path Integrals
Kerson Huang
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471141208

Book Description

A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained.

Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features:
* Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization
* A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations
* Nineteen self-contained chapters with exercises, supplemented with graphs and charts

Customer Reviews:

5 out of 5 stars Extremely solid for self-teaching.......2006-04-06

This book is an ideal introduction to quantum field theory for a graduate student. Assuming a strong background in basic quantum mechanics and classical mechanics, Huang develops quantum field in a methodical fashion. In contrast to other popular quantum field theory books (such as Peskin) Huang doesn't leave out important details, especially with regard to the mathematics behind spinor fields. Plus the book is very readable.

5 out of 5 stars A good introduction to the physics behind renormalization.......1999-05-16

A very good introduction to QFT. It starts with a rather classical account of QED, then develops renormalization and applies it mainly to statistical physics. So the text does not cover non-abelian gauge theories, and is not sufficient for readers who learn QFT for particle physics applications. But the exposition of renormalization is really excellent and complete. I liked the exceptional clarity and lucidity of most calculations, and the excellent set of problems. Solving them all extends the book's scope far beyond the table of contents.
The Science of Sound (3rd Edition)
Average customer rating: 2.5 out of 5 stars
  • A real page-turner...
  • Terrible
  • Lots of Problems
  • A good elementary textbook
  • Toned down math, but still pure sound
The Science of Sound (3rd Edition)
Thomas D. Rossing , F. Richard Moore , and Paul A. Wheeler
Manufacturer: Addison Wesley
ProductGroup: Book
Binding: Hardcover

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  1. Fundamentals of Musical Acoustics: Second, Revised Edition Fundamentals of Musical Acoustics: Second, Revised Edition
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ASIN: 0805385657

Book Description

The Science of Sound is widely recognized as the leading textbook in the field. It provides an excellent introduction to acoustics for readers without college physics or a strong background in mathematics. In the Third Edition, Richard Moore and Paul Wheeler join Tom Rossing in updating The Science of Sound to include a wide range of important technological developments in the field of acoustics. New exercises and review questions have been added to the end of each chapter to help readers study the material.

Customer Reviews:

1 out of 5 stars A real page-turner..........2006-12-09

An abundance of writing and grammatical errors do not make the already confusing explanations in this book any easier to grasp. I got bogged down in technical mistakes before I could begin to use the provided formulas. This is one of the worst textbooks I've ever read, and taking a supplemental course from one of the authors only added to one of the worst experiences of my college career.

1 out of 5 stars Terrible.......2006-02-03

This book is terrible for beginners. It doesn't explain things well. The graphs and diagrams are hard to understand and it doesn't give enough examples to help you do the exercises at the end of the chapter. Also, there are a lot of typos and errors. For instance I tried to look up "attenuation of sound" in the index and the word was there with no page number. And I found a graph where the graph didn't match the descrpition. I have the advantage of having one of the authors of the book as my professor, and I still have a hard time understanding this book. It's horrible.

2 out of 5 stars Lots of Problems.......2000-10-01

This book should have been a classic introduction to musical acoustics. Instead, it tries to hard, is convoluted, often in error, and confuses musicians.

When I taught from this book, I and the class found errors in equations, references to equations, and calculations. When undergraduates are struggling to learn, this is a very bad context.

The book is so concerned with a level of comprehensiveness, that measured clarity is left out. At the same time, for the expert, it is too little. Therefore, it appeals to neither the introductory level nor the more advanced level.

I gave up using this book.

4 out of 5 stars A good elementary textbook.......2000-08-09

I have used this book as the primary textbook for an introductory course in the physics of music. It is at a somewhat higher level than some of its competitors (e.g. "The Acoustical Foundations of Music" by Backus) but still suitable for non-science majors with weak math backgrounds. It is the most thorough and informative book I have seen at this level. However, the students complained that it was somewhat dull. Also, the section on electronic reproduction of music is out of date--relatively little on CD's etc., and nothing on mp3 and related technologies. Still, I plan to use it again.

5 out of 5 stars Toned down math, but still pure sound.......2000-06-13

I have taught a course entitled "Acoustics for Musicians and Recording Engineers" to Engineering, Music, and Film majors using Rossing's THE SCIENCE OF SOUND. He has toned down the equations enough that the students aren't groaning, yet he's remained true to the interdisciplinary nature of acoustics as a pursuit of physics, psychology, math, and engineering. The structure of the book provides a wonderful outline for the course and it has been an invaluable resource for both me and the students who have wished to continue with their study of acoustics.
3,000 Solved Problems in Physics (Schaum's Solved Problems) (Schaum's Solved Problems Series)
Average customer rating: 4.5 out of 5 stars
  • Simply Excellent
  • Amazing book, the naysayers are clueless about its real method ...
  • PERFECT
  • Schaum's Solve Problems
  • A terrific learning aid!
3,000 Solved Problems in Physics (Schaum's Solved Problems) (Schaum's Solved Problems Series)
Alvin Halpern , and Alvin Halpern
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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  4. Physics Problem Solver (Problem Solvers) Physics Problem Solver (Problem Solvers)
  5. 3,000 Solved Problems in Chemistry (Schaum's Solved Problems) (Schaum's Solved Problems Series) 3,000 Solved Problems in Chemistry (Schaum's Solved Problems) (Schaum's Solved Problems Series)

ASIN: 0070257345

Book Description

Solved Problem Series

These books help readers review and master what they've learned by showing them how to solve thousands of relevant problems. Perfect for preparing for graduate or professional exams, these detailed reminders of problem-solving techniques show readers the best strategies for answering even the toughest questions, including the types that appear on typical tests.

Customer Reviews:

5 out of 5 stars Simply Excellent.......2007-06-24

I bought this book to help my daughter with her physics class. I just wanted to help her practice with a few of the easier problems given that she is still in high school. Surprisingly, I found the book better in comparison to the problems given in her actual textbook. Obviously, one cannot learn physics from scratch by doing these problems alone. Some initial instruction is required. However, once the basic concepts of physics are learned, this in turn becomes an excellent practice guide in order to master the topics covered. No matter what your level of acheivement is, this book will help you get to the next level. I wish I had found this book a lot sooner.

5 out of 5 stars Amazing book, the naysayers are clueless about its real method ..........2007-03-05

I never bought this book, because every time I looked at it on the shelf I quickly flipped through it, and every time decided it was full of too-simple problems, essentially just the plug & chug variety, not really much to be gained by a physics student.

But my dad had bought it to study for some engineering problems he was working on, and he didn't need it, so I grabbed it, and tucked it away for a few months.

Then I gave myself the goal of working through all 3000 problems, about 25 each night. I had hoped it would help me get better at doing these kind of problems in my head and improve my accuracy, which desperately needed improving.

Here's the deal with this book ... YES it does start with problems so simple that a high-schooler can do them, and then it drills those concepts over and over, but while that's happening, Halpern gradually increases the difficulty of the problems. For all of those people that insult this book as not challenging, I'll wager they would have a hard time with many of the problems by chapter end, at which point Halpern has developed an increasingly complex problem set. And amazingly, after working all the exercises, the problem-solver can handle many or most of them.

It's like that old movie Karate Kid, where the Ralph Machio character gets mad at his teacher for making him paint the fence all day, and then his teacher shows him that all his work has actually done something.

Halpern tells you this at the beginning of the book, that the his method will make you a "master of the art -- and should do so if used properly." The proper way of course, it to struggle with the problems that are a little harder before you are tempted to peek at the answer. (I use a folded paper to cover the answer while I look at the problem.)

If you are preparing or trying to learn all of physics, then you should skip around from chapter to chapter, rather than trying to work through a chapter at a time. This helps you synthesize a variety of information better.

There are a few typos and a few errors, but they are pretty easy to catch. And the redundancy of the problems makes errors less critical anyway.

(Halpern was a professor at my school for my MA in physics, City University of New York, although I never met him. I would like to meet him someday for helping me to become a master, although I still have a long way to go.)

5 out of 5 stars PERFECT.......2007-01-13

Just like it was 30 years ago. Plenty of solved problems to self learn Physics.

3 out of 5 stars Schaum's Solve Problems.......2006-11-06

The information in this problem book are many and some pertain to all physics have similar concepts in the way Alvin Halpen,PH.D has structure this book. Yet, for the newcomer in Physics will not easily understand. This book for resource and problems is fair!But not recommended!

5 out of 5 stars A terrific learning aid!.......2006-07-08

This book has exactly what it says in the title. The problems are well-chosen, and the detailed solutions are written in a way that really aids learning. (The "canned" solutions for many textbooks are full of references to obscure equations that are worked out in the chapter, and so promote a "flip through the pages hunting for the right equation" method of problem solving, which does not lead to strong problem solving competency. In contrast, the solutions in this book start from fundamental equations, the approach used by most good teachers, at least at the college and university level, and they are very well-written.)
There are no explicit review sections, so that this is a supplement to a regular text, rather than a replacement for it. (Review of some particularly difficult concepts _is_ covered via the mechanism of essay-style questions.)
Of course, to get the benefit of this text, you must try to work the problems on your own, before looking at the solutions. This is the best textbook supplement I've yet seen -- buy it, work as many of the problems as you possibly can, and it will _really_ help!
(This review written by a college physics prof.)
Mirror Symmetry (Clay Mathematics Monographs, V. 1)
Average customer rating: 5 out of 5 stars
  • Detailed overview of the subject
Mirror Symmetry (Clay Mathematics Monographs, V. 1)

Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Hardcover

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ASIN: 0821829556

Book Description

This thorough and detailed exposition is the result of an intensive month-long course sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives. The material will be particularly useful for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics.

This one-of-a-kind volume offers the first comprehensive exposition on this increasingly active area of study. It is carefully written by leading experts who explain the main concepts without assuming too much prerequisite knowledge. The book is an excellent resource for graduate students and research mathematicians interested in mathematical and theoretical physics.

Customer Reviews:

5 out of 5 stars Detailed overview of the subject.......2005-05-16

Mirror symmetry has become an established branch of mathematics and mathematical physics, and research in the subject has resulted in brilliant developments. This sizable book contains essentially some (polished) lecture notes of a seminar series in mirror symmetry that was given in the spring of 2000. This reviewer only studied Part 5 of the book, entitled "Advanced Topics" and so only that part will be reviewed here. In addition, space constraints then dictate only a small portion of this part can be reviewed. Needless to say, any reader who intends to tackle this book will need a substantial background in modern mathematics and advanced physics, and a sizable commitment in time. The time spent is well worth it though, as both the mathematics and physics behind mirror symmetry has to rank as one of the most fascinating research topics in the last two decades.

In the chapter entitled "Topological Strings" the authors consider the functional integration of worldsheet geometries. This project involves essentially the integration over the complex structures of Riemann surfaces. Referring to this procedure as "quantum gravity", they do not address it in-depth, but instead focus on the coupling of topological sigma models to worldsheet gravity, which is called `topological string theory' in the literature. The authors first consider the case where the target is a Kahler manifold whose first Chern class is zero, since for this case the quantum cohomology ring is less easy to obtain, i.e. it can obtain contributions from holomorphic maps of any degree. Even for the case where there is no coupling to gravity, the degree 0 contribution is related to the classical intersection number. The contributions from higher degree result in the deformation of the classical cohomology ring into the quantum cohomology ring. The authors then ask whether there are any other correlators that will give nontrivial (non-zero) invariants in genus 0. Posing this question leads to the WDVV equation and the genus 0 topological string partition function. The n-point correlation functions of topological strings can then be defined as the nth partial derivatives of this function. For higher genus cases, the correlators are all zero, but the authors show the connection between the higher genus partition function and holomorphic anomalies. The case of three-dimensional Calabi-Yau manifolds is special, if one concentrates on the integration over the complex structures of the worldsheet. When the complex dimension of this moduli space is 3(g-1) then there are isolated points where holomorphic maps exist. Defining a topological string theory for Calabi-Yau threefolds is straightforward, as the author shows, and proceeds analogously to the case of topological field theory. A measure is defined on the moduli space of Riemann surfaces of genus g that cancels the axial charge anomaly. A genus g (>1) topological string amplitude, which is a section of a bundle over the moduli space of Calabi-Yau manifolds, is then obtained from this procedure. Modulo the presence of holomorphic anomalies, the authors show that the definition of topological string amplitudes is consistent with the topological symmetry. The origin of these holomorphic anomalies is discussed in fair detail by the authors, having their origin in the boundaries of the moduli space.

The rigorous mathematical formulation of mirror symmetry is of course of great interest to mathematicians. Because of its origin in string theory and quantum field theory, mirror symmetry has not yet received this kind of rigor. Chapters 37 and 38 of this book discuss some of the approaches that attempt to put mirror symmetry on a more rigorous foundation. One of these involves the use of `derived categories,' an approach that was recommended by the mathematician Maxim Kontsevich. The discussion in these chapters takes place in the context of D-branes, and Kontsevich conjectures that mirror symmetry is the equivalence of two categories: the derived category of coherent sheaves, and the category of Lagrangian submanifolds with flat U(1) connections. Specifically the equivalence entails the equivalence between the bounded derived category of coherent sheaves or `B-cycles' and the category of A-cycles with compositions defined in terms of holomorphic maps from disks. This latter category is derived from the Fukaya A-infinity category, as is shown by the authors. They discuss in detail this category, being essentially a generalization of a differential, graded algebra, especially how to obtain the compositions. In chapter 37, the authors give an explicit example of the equivalence of these categories for the case of the elliptic curve. The elliptic curve is interesting in this regard in that it is its own mirror, i.e. the complex parameter is mapped to the complexified Kahler parameter by the mirror map.

The derived category has sometimes been a stumbling block to those who want to understand the Kontsevich conjecture. The authors do not attempt to give the reader the needed insight into this kind of category, but merely take it to be a collection of all holomorphic bundles and coherent sheaves. Sheaves in this category can be subtracted from each other using a map between them. Physically, this subtraction corresponds to the annihilation of branes and anti-branes via a tachyon. Derived categories though are straightforward to think about if one views them from the standpoint of algebraic topology. Derived categories are rich enough to include notions of localization and triangulated objects (i.e. "complexes") and maps (i.e. morphisms) between these objects. This is a kind of "homology" but what is of main interest are homotopies between the morphisms. The class of homotopic morphisms between two complexes forms an abelian group and one can then obtain a category consisting of complexes as objects and classes of homotopic morphisms as morphisms. A cohomology functor can then be defined on this category, along with graded objects and differentials between them. The homotopic category can be given a "triangulation" and morphisms in this category that give rise to isomorphisms in cohomology are given special status, called `quasimorphisms.' The localization of this category with respect to quasimorphisms is called a derived category.

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