An Introduction to Quantum Field Theory (Frontiers in Physics)

Customer Reviews:

Perfect........2007-08-10

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

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.

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.

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.

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.

Deep Down Things: The Breathtaking Beauty of Particle Physics

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Particle Physics Made Easy
A Review From a Non-Physicist
It really is "Breathtaking"
A 'big-picture' conceptual guide to the Standard Model
Best popular particle/quantum physics books I have read

Deep Down Things: The Breathtaking Beauty of Particle Physics
Bruce A. Schumm
Manufacturer: The Johns Hopkins University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 080187971X

Book Description

A useful scientific theory, claimed Einstein, must be explicable to any intelligent person. In Deep Down Things, experimental particle physicist Bruce Schumm has taken this dictum to heart, providing in clear, straightforward prose an elucidation of the Standard Model of particle physics -- a theory that stands as one of the crowning achievements of twentieth-century science. In this one-of-a-kind book, the work of many of the past century's most notable physicists, including Einstein, Schrodinger, Heisenberg, Dirac, Feynman, Gell-Mann, and Weinberg, is knit together in a thorough and accessible exposition of the revolutionary notions that underlie our current view of the fundamental nature of the physical world. Schumm, who has spent much of his life emmersed in the subatomic world, goes far beyond a mere presentation of the "building blocks" of matter, bringing to life the remarkable connection between the ivory tower world of the abstract mathematician and the day-to-day, life-enabling properties of the natural world. Schumm leaves us with an insight into the profound open questions of particle physics, setting the stage for understanding the progress the field is poised to make over the next decade or two.

Introducing readers to the world of particle physics, Deep Down Things opens new realms within which are many clues to unraveling the mysteries of the universe.

Customer Reviews:

Particle Physics Made Easy.......2007-03-02

This book should be a must read for anyone that tries to understand particle physics. I've been looking for something like this for a long time. The Standard Model is explained with great skill and clarity, and with minimal use of math. This is not a mathematical book, but where minimal mathematics becomes necessary (group theory), it is introduced with the assumption that the reader knows next to nothing (which was my case) and developed to the point where, combined with physics, it makes sense. Most of the math only requires logic, not computations, and all you are required to memorize are a few rules -- conventions -- that only take a couple of lines. Beautiful.
The author limits himself to what is known and generally agreed about particle physics. The limits of the theory are also very well explained, but no significant steps into the unknown are made, which I think it is a good thing for once.
If you like Brian Greene, Michio Kaku, Lisa Randall, and others like them, do them, and yourself, a favor: read "Deep Down Things". It will open new horizons in the way you see, and appreciate, their work. These more popular authors cross into the unknown with beautiful, breathtaking constructs, but none explains the basics as Bruce Schumm does.

A Review From a Non-Physicist.......2007-01-01

Two items set this lay physics book apart: clarity of writing and minimum of speculation. It covers only material amenable to experimentation. This rules out both string theory and multiple universes - each mentioned only briefly. Nor does it dwell on Einstein's theories of special or general relativity - the gravitational physics of the large. "Deep Down Things" is like an introductory text on quantum phenomenon and particle physics without the explicit math and with more explicit wordage.

Particle physics studies the smallest units of matter and how they interact with each other. This led to ever larger particle accelerators during the last 68 years of the 20th century. More than 150 exotic particles have been discovered - every one having differing combinations of properties that boggle the mind. An exotic particle that results from the collision of two protons may exist for only 10 to the minus 12 seconds before it decays into something else. Traveling at close to the speed of light, this is just enough time to leave a (highly sought after) 1 mm mark on a recorder, documenting the brief life of that particle. The Particle Data Group from Berkeley exists just to keep physicists updated on these particles.

For something so fleeting, why do we bother? Because this research is centerstage in explaining the Big Bang and all of cosmology. As by-products, we achieved huge gains in any industry you can name. Unless you live like a Mennonite or are on a boy scout camp-out, these technologies effect the way you live your daily life - ground floor activity on the internet itself came about because physicists desired a more immediate way to share research with each other.

The use of common sense was not a factor in the investigations of particle physics. Instead, knowledge was and is gained through particle accelerators, predictions from abstract mathematical models, and meticulous use of the scientific method by thousands of physicists. The author mentions frequently that the math works out, predicts something, disproves something, needs a cheat factor, etc. This made me want to see the math, but I'm at least a couple of college courses from there, so I guess I'll have to take his word for it. For non-physics, non-math majors, consider reading on despite lack of total understanding or you might bog down in details. As the point of view changes, concepts are restated and you'll get another stab at it. The author starts a sentence on page 187, "If you've understood, even vaguely..." and ends it with "it gets even better (or worse...) as we move on to other properties of elementary particles."

On page 351, he closes with congratulations to anyone who made it to the end - then inserts a joke about the Higgs field that only an "insider" (a physicist or one who read the book) would understand. This is a great book that I highly recommend for any physicist who wants to brush up on particle physics, any undergrad or grad student in physics, or any other scientist types who are persistent enough to want a better handle on this fascinating but difficult subject.

It really is "Breathtaking".......2006-11-30

This is a book about quantum mechanics, and gauge theory in particular. It's essentially non-mathematical, having just a few equations, and requires little mathematical expertise. For readers with math anxiety, or those unfamiliar with partial differential equations, the few equations in the book can be skipped without missing much, as Schumm focuses almost exclusively on providing a qualitative understanding of what's at the heart of the Standard Model of quantum mechanics.

This isn't your typical book on quantum mechanics, aimed at your typical armchair scientists. There's virtually no discussion about various speculative macroscopic aspects of QM, such as freewill. God doesn't come into the picture except as a non-personal synonym for "the universe." Schrödinger's cat isn't discussed. Neither is tunneling, time travel, teleportation, or Bell's inequality. This text is what I'd describe as a nuts-and-bolts qualitative look or introduction to the Standard model. I think it would be excellent reading for anyone contemplating a class in QM, before taking a quantitative and detailed course on the subject. Of course, I'd also recommend it for casual yet serious readers who want to know the basis for modern quantum theory.

The first half of the book lays the groundwork with a discussion of forces of nature, patterns, the building blocks of nature, and symmetry. I particularly liked Schumm's explanation of how symmetry relates to conserved quantities. I think he does an especially nice job of describing Lie groups and segueing the topic into the heart of this book, which is gauge theory.

The gauge principle says that objects within a system are subject to precise laws of interaction. It also says that the wave equation is invariant with respect to local changes in phase. The connection between these two notions (phase invariance and laws of interaction) provides a quantitative theory for causation, known as the gauge principle. [pp. 276-277] I commend Schumm for presenting the basic principles and arguments of gauge theory in a way that can be clearly understood at a qualitative level. Here's a summary of how he does it.

Start with the Schrödinger wave equation. Next, apply the condition that information cannot be instantaneously transmitted or transmitted with arbitrary speed over arbitrary distances. This is a principle that seems deeply ingrained in Einstein's relativity, that no object with non-zero mass energy can travel faster than the speed of light, and is the position taken by Yang and Mills in their 1954 paper in the Physical Review, where they argue the following:

"As usually conceived, however, this arbitrariness is subject to the following limitations: once one chooses [the phase of the wave function] at one space-time point, one is then not free to make any choices at other space-time points. It seems that this is not consistent with the localized filed concept that underlies the usual physical theories. In the present paper we wish to explore the possibility of requiring all interactions to be invariant under independent [choices of phase] at all space-time points. [p. 217-218]

Back to the Schrödinger wave equation, Schumm considers the case of an isolated electron (no potential). To make the wave function invariant with respect to local changes in phase, Schumm describes a trick used by Yang and Mills, in which they added a new term to the wave equation, a so-called "cheating" term, A(x). A(x) changes when the phase of the wave function changes, in just the right way so that the overall wave function is unaltered by local changes in the wave function's phase. This might seem like an obvious and trivial thing to do, but interestingly, when you do this you find that the cheating function, A(x), represents the quantum of the electromagnetic field - the photon. As Schumm explains:

"The inclusion of A(x) thus incorporates, within the field-theoretical description of the particle's behavior, the possibility that the particle emits or absorbs a photon, that is, the possibility that the particle emits or absorbs a quantum of the electromagnetic field."

This is a nifty trick. Start with the Schrödinger equation for an isolated particle, apply the relativity principle by insisting on invariance of local phase shifts, add a "cheating" factor to make phase invariant, and the "cheating factor" ends up being the quantum force mediator of the particle described by the Schrödinger equation. The nature of the cheating term depends on the symmetry of possible changes to the wave function. That's where Lie groups come in, and that's why it's so helpful the way Schumm lays the conceptual foundation with his chapter on Lie groups.

Mathematically, the symmetry of a quantum particle is described by the Lie group that describes possible changes to the particle's wave equation. If the group has only simple phase-change symmetry we end up with quantum electrodynamics, or the quantum theory of the electromagnetic force. For wave functions described by more complicated Lie groups (wave equations that have rotational symmetry in some internal symmetry space), we must add different cheating terms, as many as there are generators of the Lie group. This is the basic idea behind the gauge principle, which is at the heart of the Standard model of quantum mechanics. Of the four known forces of nature, three (electromagnetic, weak nuclear, and the strong nuclear interactions) are explainable from the well-established methods of gauge theory.

This was one of the best books I've read this year. It's long (just short of 360 pages) with lots of material between the covers. You'll want to read the Appendix and notes, and you'll most likely find yourself reading over parts of the book several times, digesting the meaning behind the words. In the end, I think you'll agree with the author's assessment that quantum mechanics - the study of "deep down things" really does reveal a breathtaking beauty of the natural world.

A 'big-picture' conceptual guide to the Standard Model.......2006-08-28

Fed up with useless metaphors which equate the Higgs particle with hangers-on at a party slowing a celebrity's passage? Exasperated at continual references to Lie algebras and gauge theories, which are never explained?

In Peter Woit's recent book `Not Even Wrong', he comments (p. 205) that relativistic quantum field theory is not even studied until the second or third year of graduate school. For the rest of us, there is `Deep Down Things'.

Schumm's objective is to take us on a conceptual tour of the Standard Model of quantum mechanics, without requiring a mastery of the technical apparatus. The first half of the book introduces the four fundamental forces, wave-particle duality and the wave function itself. The approach is historical and visual - plenty of Feynman diagrams - and Schumm assumes the reader is happy with complex exponentials. By chapter 5 we are deep in the eightfold way, and the classification of quarks, leptons (electrons, muons, neutrinos) and bosons (the force quanta).

Chapter 6 begins the process of diving deeper with a discussion of Lie groups and Lie Algebra, motivated by plenty of examples. A Lie group is defined via: (i) a continuous set (i.e. a real or complex manifold such as R^n or C^n) with (ii) operators which are continuous functions over the manifold. Chapter 7 introduces Noether's theorem: `To every differentiable symmetry generated by local actions, there corresponds a conserved quality' and this is linked with symmetries under transformations by the Lie group operators (such as rotations in isospin space which interchange protons and neutrons).

Introductory quantum mechanics courses talk about the physical irrelevance of the phase of the wave function when it comes to the calculation of probabilities of observables. We thus have the concept of global phase invariance. However, this is unphysical - we cannot have the universe adjusting phase by the same amount everywhere at the same time. Yang and Mills in the mid-50s proposed to force the wave function to be invariant under local changes of phase: it turns out the only way to achieve this is to add a new term of the form gA(x)psi(x) where g is a charge parameter associated with the particle, psi(x) is the wave function and A(x) is a new term which turns out to be the field potential function for the relevant force field (electromagnetic in chapter 8). The freedom of choice in choosing the function A is called a gauge freedom, hence gauge theory.

Choose a fundamental particle. Write down its wave function. Identify the spaces in which the particle participates (space-time, isospin, ...). Identify the Lie group which rotates the wave function (state vector) in each of these spaces - U(1), SU(2), SU(3). By the principle of local phase invariance, adjust the original wave function with gauge terms gA(x)psi(x) as above. From making this work mathematically, out pop the corresponding force quanta (= the number of generators of the corresponding Lie algebra above). As the chapter heading puts it: `Physics by Pure Thought'!

Chapter 9 explains how the standard model assigns a mass of zero to all force-field quanta. Any attempt to add mass destroys the local phase invariance that we just discussed. The only way to retrieve the situation is to assume the existence of a new field (the Higgs field) which somehow pervades the universe and which interacts with non-zero-mass force quanta (via the weak force) in a `screening' way which gives them mass. The Higgs field is also responsible for the masses of quarks and leptons. If this is true, there should be a Higgs particle within reach of CERN's Large Hadron Collider in 2007.

This is a really excellent book. If you dimly recall how to solve a differential equation, and are unfazed by the notion of an abelian group, then this book is accessible. By book-end you have the sense that you `get' the big picture of the standard model and its remaining conceptual weaknesses. I would say that if you were an undergraduate interested in theoretical physics and wanted a tour d'horizon, this is the one book which will give it (Penrose's `The Road To Reality' is still too difficult for this purpose).

Best popular particle/quantum physics books I have read.......2006-05-02

Bottom line: Buy it.

If you are tired of books that throw out words like "symmetry" and "gauge theory" without ever explaining (at least conceptually) what these terms mean and how these concepts relate to a deep understanding of particle physics then this is the book to buy.

The author explains the mathematical concepts quite simply and in such a way that if you can read ANY popular book on physics then you can understand how Lie Algebras and Gauge Theories help derive the eightfold way, the charges on some bosons, the probability of the Higgs field/particle, and therefore lead to the Standard Model of particle physics.

Imagine a book which covers these topics (Lie Groups, Lie Algebras and Gauge Theories) without ever seeming mathematically challenging or complex. Here it is.

My only disappointed? It doesn't cover more, because this is the best exposition -- real teaching at a world class level -- of the subjects it does cover. If Schumm ever writes another book I will buy it, sight unseen.

If you have read, or wanted to read "The Road to Reality" by Penrose (which I highly recommend if you have the determination to read it), this will make several sections of that book much easier to understand -- were all of Penrose's explanations as high quality as "Deep Down Things" there would likely never be a better book on these subjects.

For anyone considering this book, the answer is simple: buy it and enjoy reading it.

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Excellent reference work
Introduction to strong interaction.

Quantum Chromodynamics
Walter Greiner , Stefan Schramm , and Eckart Stein
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540485341

Book Description

The book is a self-contained introduction to perturbative and nonperturbative Quantum chromodynamics (QCD) with worked-out exercises for students of theoretical physics. It will be useful as a reference for research scientists as well. Starting with the hadron spectrum, the reader becomes familiar with the representations of SU(N). Relativistic quantum field theory is recapitulated, and scattering theory is discussed in the framework of scalar quantum electrodynamics. Then the gauge theory of quarks and gluons is introduced. In the more advanced chapters, perturbative and nonperturbative techniques in state-of-the-art QCD are discussed in great detail.

The new third edition has been extensively revised and enlarged to cover all new aspects in Quantum chromodynamics.

Customer Reviews:

Excellent reference work.......2007-01-17

This is a must have for any physics enthusiast, student and professional physicist alike! It's very complete on the topic.

Introduction to strong interaction........2000-04-08

This may be one of the best textbooks about the topic. However, the translation is not done properly. The new edition is supposed to be published three years ago with corrections to the major errors, but the publication date has been postponed several times and it is still not available today. Anybody capable of reading German is recommended to read its original edition in German.

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Excellent

Quarks, Leptons and Gauge Fields
Kerson Huang
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810206593

Book Description

This is perhaps the most up-to-date book on Modern Elementary Particle Physics. The main content is an introduction to Yang-Mills fields, and the Standard Model of Particle Physics. A concise introduction to quarks is provided, with a discussion of the representations of SU(3).

The Standard Model is presented in detail, including such topics as the Kobayashi-Maskawa matrix, chiral symmetry breaking, and the q-vacuum. Theoretical topics of a more general nature include path integrals, topological solitons, renormalization group, effective potentials, the axial anomaly, and lattice gauge theory.

This second edition, which has been expanded, incorporates the following new subjects: Wilson's renormalization scheme, and its relation to perturbative renormalization; pitfalls in quantizing gauge fields, such as the Gribov ambiguity; the lattice as a consistent regularization; Monte Carlo methods of solution; and the issues, folklores, and scenarios of quark confinement. More than a quarter of the book comprise of new materials.

This book may be used as a text for a one-semester course on advanced quantum field theory, or reference book for particle physicists.

Customer Reviews:

Excellent.......1998-04-23

This is by far one of the best introductory texts on this rapidly changing field. I especially enjoyed the lucid treatment of topological objects in quantum field theory. One of the most appealing qualities of the book was the author's concise, to-the-point style. Very recommendable.

An Introduction to Gauge Theories and Modern Particle Physics (Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology)

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A clear and well thought out treatment

An Introduction to Gauge Theories and Modern Particle Physics (Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology)
Elliot Leader , and Enrico Predazzi
Manufacturer: Cambridge University Press
ProductGroup: Book
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ASIN: 0521499518

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Volume 2 deals at some length with CP-violation, but is mainly devoted to QCD and its application to "hard" processes. The authors briefly cover "soft" hadronic physics, also. This work will provide a comprehensive reference and textbook for all postgraduate students and researchers interested in modern particle physics.

Customer Reviews:

A clear and well thought out treatment.......1998-09-16

Leader and Predazzi have written an exsellent text for graduate students. They cover the wide range of topics in great clarity. Especially in the chapter about renormalization they succeed in presenting the core in detail without technical obfuscation.

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Classical Fields
Moshe Carmeli
Manufacturer: World Scientific Publishing Company
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Binding: Hardcover

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ASIN: 9810247877

Topology, Geometry, and Gauge Fields: Interactions (Applied Mathematical Sciences)

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correction to dost
Easy reading, complete proofs, plenty of exercises
Don't waste your money
MATH AND TOPOLOGY
required reading for a topologist interested in physics

Topology, Geometry, and Gauge Fields: Interactions (Applied Mathematical Sciences)
Gregory L. Naber
Manufacturer: Springer
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ASIN: 0387989471

Book Description

This book covers topology and geometry beginning with an accessible account of the extraordinary and rather mysterious impact of mathematical physics, especially gauge theory, on the study of the geometry and topology of manifolds. Much of the mathematics developed in the book to study the classical field theories of physics (de Rham cohomology, Chern classes, Semi-Riemannian manifolds, Cech cohomology, spinors etc.) is standard, but the treatment always keeps one eye on the physics and unhesitatingly sacrifices generality to clarity. The author brings the reader up to the level needed to conclude with a brief discussion of the Seiberg-Witten invariants. Although this volume can be read independently Naber carries on the program initiated in his earlier volume, Topology, Geometry and Gauge Fields: Foundations, Springer, 1997, and writes in much the same spirit with precisely the same philosophical motivation. A large number of exercises are included to encourage active participation on the part of the reader. This work will be of great interest to researchers and graduate students in the field of mathematical physics. REVIEWS OF TOPOLOGY, GEOMETRY, AND GAUGE FIELDS: FOUNDATIONS "It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics...Naber combines a knowledge of his subject with an excellent informal writing style." NZMS NEWSLETTER "...this book should be very interesting for mathematicians and

Customer Reviews:

correction to dost.......2006-05-20

The review "Easy reading, complete proofs, plenty of exercises, October 29, 2005 by Rehan Dost is of the first volume, Foundations, not this volume which is Interactions. Naber's books are crafted to bridge physics, undergraduate mathematics and graduate mathematics. This is one more of his beautiful volumes in applied mathematics.

Easy reading, complete proofs, plenty of exercises.......2005-10-30

This text is by far the best introductory text marrying basic concepts of physics with pure mathematics.

Some background in the basic concepts of vector calculus, linear algebra, complex numbers and group theory is required.

The author begins by motivating the mathematics by the pursuit of finding a vector potential to represent a magnetic monopole. We see that the topology of R3-0 precludes such a vector potential from existing. We see here a simple example of how the topology of a space affects the physics associated with it.
The importance of the vector potential as something other than a convenient computational tool is highlighted by a reference to essential inclusion in quantum mechanics. Thus we NEED such a potential.

The author now asks whether there is a "trick" or device to get around this difficulty. The device are principal bundles and connections. For example the potentials noted above must keep track of the phase of a charged test particle as it moves thru the field of a magnetic monopole. We need a "bundle" of circles ( representing the phase at each point ) over S2 ( the author explains why we need only consider S2 instead of R3-0, briefly we need only keep track of 2 of the 3 spherical co-ordinates ).
Thus a curve in S2 thought of as the particles trajectory will have to be "lifted" to the bundle space by a lifting procedure called a connection.
In a more general setting elementary particles have an internal structure ( spin etc ) which becomes apparent during interactions although may not be apparent in uniform motion thru a vacuum. Since the phase of the particle does not alter the modulus when calculating probabilities these do not change. However, when the particles interact phase differences are important. We need to keep track of such phases as the particles interact.

Thus we need a "bundle" over a 4-manifold ( keeps track of the particles space-time path ) to keep track of such internal states. One sees we also need a group to transform states into one another ( usually incorporated into the bundle ). Connections then model physical phenomena which mediate changes in the internal states.
We see that some connections satisfy the Yang-Mills equations and using the appropriate equivalence relation form Moduli spaces.

Now that may seem like alot to digest with only a spattering of mathematical maturity.

The beauty of the book is that the author starts from FIRST principles.

Chapter 1 introduces topological concepts of topology, continuity, quotient topology, projective spaces, compactness, connectivity, covering spaces and topological groups.

Chapter 2 introduces concepts of path lifting, fundamental groups, contractability, simple connectedness, covering homotopy theorem, higher homotopy groups

Chapter 3 introduces principle bundles, transition functions, bundle maps and principle bundles over spheres.

Chapter 4 introduces manifolds, derivatives on manifolds, tangent/cotangent spaces, submanifolds, vector fields, matrix lie groups, vector valued 1- forms, 2 forms and Riemann metrics

Chapter 5 gets to some physics with gauge fields and connections, curvature, Yang-Mills functional, moduli spaces, Hodge dual , matter fields and covariant derivatives.

At each step the author carefully provides complete proofs and easy exercises to ensure understanding.

It was a pleasure to read the book and complete the exercises. At no point did I feel frustration or boredom.

Don't waste your money.......2004-08-27

This review refers only to the book printing quality not to the contents.

I had purchased some books from Springer in the past (Like Arnold Mathematical Methods of Classical Mechanics, Lang Algebra etc..) and found them beautifully edited: good binding, paper etc..

And to my surprise I was very disappointed with the overall quality of this book, poor binding -glued instead of sewn- bad quality paper -forming waves at the binding spine, etc..

You pay for a quality item, a book you can use for years, and you get a hardbound crap that you can not left open in a table without holding it tight risking to lose the pages after a few days of use in the process.

I find this unacceptable in books costing 60$+. Sadly I find this to occur very often, publishers should be more careful with their printings and custumers should demand a better quality.

Don't waste your money.

A reader.

MATH AND TOPOLOGY.......2001-05-08

Topology is very important scince in the fields of mathematics. And it using in many of another sinceis.

required reading for a topologist interested in physics.......2000-05-14

As a mathematician turned physics grad student, it is often difficult to read "Math for Physicists" books simply because of the focus on making "numbers churn out;" which, at least for me personally, more difficult to get a handle on the subject and then, in turn, use it fruitfully.

This book on the other hand, is exemplary of why I got into physics in the first place. The first chapter (Physical motivations) and the last chapter (Gauge Fields and Instantons) can be read by any one with undergraduate topology under their belt and come away with a more powerful understanding of gauge theory than, in my opinion, can be found in other introductory gauge theory texts I've been directed to.

Of course I'll read all those said texts as well, but I'm thankful that I found this one.

Average customer rating:

A useful reference text for gauge theory.

Spivak on Steroids

A mathematically tight and well-motivated work

Clean and modern exposition

This book is all that is bad about abstract mathematical physics writing

Gauge Theory and Variational Principles
David Bleecker
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486445461

Book Description

Detailed and self-contained, this text supplements its rigor with intuitive ideas and is geared toward beginning graduate students and advanced undergraduates. Topics include principal fiber bundles and connections; curvature; particle fields, Lagrangians, and gauge invariance; inhomogeneous field equations; free Dirac electron fields; calculus on frame bundle; and unification of gauge fields and gravitation. 1981 edition

Customer Reviews:

A useful reference text for gauge theory........2007-07-28

A useful reference text for gauge theory. While Bleecker includes an introductory chapter to cover prerequisites (tensor analysis, differential forms, Lie groups etc) the text assumes some familiarity with these techniques and gauge theory. The text is in the "definition, theorem, proof" format. Bleecker gives fairly detailed proofs which help the reader to follow most steps. The text is short and the price reasonable, so the absence of second quantization gauge potentials, for example, is perhaps understandable. While there are chapters on gauge invariance and Action density I found the material didn't go into the detail I was looking for on invariance problems (discussion of theorems of Noether, Caratheodory's methods, Lie algebras and groups). I rated this text lower because of the complete absence of exercises and the limited references and bibliography (about three pages in total).

Spivak on Steroids.......2007-02-24

As the title suggests this "text" serves as an introduction to the QFT and guage theories recast in the "modern" mathematical setting of differential geometry.
This book is only 167 ( 1/2 regular size paper ) pages long. Although self-contained I highly recommend the reader have a working knowledge of QFT and at least an introductory course in GR. The mathematical tools of the reader should include a course in analysis on manifolds at the Spivak level or higher, acquintance with fibre bundles and basic lie groups. For example in the first chapter ( 22 pages ) the author covers differential forms, manifolds, Stokes theorem, lie derivative, deRham cohomology, lie groups and algebras. The next 20 page chapter covers principal bundles and connections ( 3 definitions all shown to be equivalent and these turn out to be the physical equivalent of gauge potentials ) followed by lie algebra valued forms, exterior covariant derivative curvature and the structure equation.
Chapter 3 defines particle fields as mappings from the principal bundle to a vector space which are equivariant or to the space of sections of the associated vector bundle. We now see that guage transformations are nothing more but the automorphisms of the bundle with certain requirements. Langrangians are developed as mappings of the space of 1 jets to the reals. G invariance of langrangians is defined and is shown to be an insufficient criteria for invariance under gauge transformations. However, we see that introduction of a connection and hence covariant exterior derivative on the bundle our Langrangian becomes gauge invariant.
The next chapter introduces action densities and shows that a particular particle field obeys the principle of least action iff it is stationary which is true iff Langrange's equation holds. There is alot of mathematical notation and machinery developed here. At this stage spin zero electrodynamics are treated.
Current are defined on PFB and a conservation of charge for g-invariant Langrangians with stationary particle fields is shown to be true. This chapter introduces the "self interaction" term for the gauge field and shows that a particle field and connection ( gauge potential ) obey the principle of least action iff they satisfy BOTH langrange equation and the inhomgeneous field equation.
The next chapter introduces spinor bundles ( to add spin particles to our repretoire ) requiring modifications of the previous mathematical tools leading to the appropriate Langrangian. Lagrange's equation is shown to reduce to the dirac free field equation.
The next chapter shows how to deal with interactions between the particle fields with spin and guage fields. This requires "spliced bundles" ( one where the particles with spin live and the other where guage fields live ) which requires another straight forward modification of our mathematical tools...redefining particle fields, Langrangians, currents, and action densities in the process. We see that in this general setting the particle fields and gauge potentials ( connection ) are stationary ( satisfy principle of least action ) iff they satisfy two generalized versions of lagranges equation and an inhomegeneous field equation. The author shows how these reduce the the special cases of the dirac electron field and yang mills field to the dirac and yang-mills equations and the inhomegeneous maxwell and yang-mills equations, respectively.
Chapter 8 goes over the mathematics of general relativity in about 10 pages.
Chapter 9 attempts to unify gauge theories and gravitation showing that the Einstein field equations and the Yang-Mills equations follow from a single variational principle dependent upon the scalar curvature of the metric defined on a suitable PFB. Problems of this unification are explained.
The final chapter explores symmetry breaking monopoles and instantons.

As you can see there is alot to absorb with the prerequisites noted above.
The book has no examples or exercise but each theorem is proved. There is also a page with corrections which is refreshing and a page summarizing the notation and page they are first introduced.

A mathematically tight and well-motivated work.......2006-07-06

Professor Bleecker has succeeded in writing a book for mathematicians and physicists. And, it's all there. I would rate this work 5-star, except I fear some physicists might find the mathematical format a bit tough (definition, theorem, lemma, etc.) As a mathematician studying physics I hope I am wrong. I find this book user-friendly due to its formality and "compactness". I caution those w/o a fair degree of mathematical acumen that this big, little book is a good deal more formal than, say, Gilmore's "Lie Groups, Lie Algebras, and Some of their Applications." But, then we all must bite the bullet. With effort, I think you will find this a chewable bullet.

Clean and modern exposition.......2006-06-19

Despite what another reviewer said, this book uses standard differential geometry notation. The notation is of the invariant (no index) style of Kobayashi and Nomizu.
I find it a delightful little book. It should be good for anyone with a background in manifold theory and Lie groups.

This book is all that is bad about abstract mathematical physics writing.......2006-05-16

Am I new to gauge theory: no.
Why does he make me feel I am?

Are these new generalized symbols really necessary to his treatment.
Apparently the author believes that rather than use words to explain
theorems...
He can rely almost entirely on this new set of symbols
that he has used to translate gauge theory to fiber bundles.
Why is it that so many times
the reader is the one who is made to do the work
of teaching himself and learning new "languages"
when the author claims he will be teaching you?

I feel that I have to warn the reader, that although he claims to be "mainstream"
differential geometry, he lies.
he uses very non-standard ( at least for the papers I've read)
notation and instead of starting at the simple gives the most abstract examples
of the notation even in chapter "0".

I grade this book as a "F"... way below even the worst
group theory book I have by an English set of professors!
I'm really as sorry as I can be, but he got me for the money,
by false advertising...
It is a very badly written book,
more a "show off"... see what I can do book,
than a I will teach you to understand book.
I had to go back to other books to compare the notation
so many times that I stack them with this book.
I spent half a year plotting solitons in Mathematica,
and I don't recognize anything in his treatment of them.
Monopoles and Instantons are even worse in this book, if possible.
It is not that I I don't believe he is using correct mathematics,
it is just that it is so hard to tell if he is!
Roger L. Bagula

Gauge Field Theories: An Introduction with Applications

Average customer rating:

Excellent

Gauge Field Theories: An Introduction with Applications
Mike Guidry
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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ASIN: 047135385X

Book Description

Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises.

Customer Reviews:

Excellent.......2001-11-01

This book is very nice. Not only does it present the theory and give problems, the problems are solved in the appendix (for the most part) and many references are cited, allowing the reader to review work elsewhere. If you are interested in quantum fields and gauge theory, I would suggest reading and working out of this book.

Average customer rating:

best choice - occasional errors - disconcerting jumps
weak interaction and unified theory.

Gauge Theory of Weak Interactions
Walter Greiner , and Berndt Müller
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540676724

Book Description

Gauge Theory of Weak Interactions treats the unification of electromagnetic and weak interactions and considers related phenomena. First, the Fermi theory of beta decay is presented, followed by a discussion of parity violation, clarifying the importance of symmetries. Then the concept of a spontaneously broken gauge theory is introduced, and all necessary mathematical tools are carefully developed. The "standard model" of unified electroweak interactions is thoroughly discussed including current developments. The final chapter contains an introduction to unified theories of strong and electroweak interactions. Numerous solved examples and problems make this volume uniquely suited as a text for an advanced course. This third edition has been carefully revised.

Customer Reviews:

best choice - occasional errors - disconcerting jumps.......2006-05-18

As of early 2006, this is the best available choice for a text on the standard model of the weak force, and the possibilities for it's upgrade with the new neutrino discoveries.

The minimum requirements for a reader are an advanced knowledge of engineering-level calculus, basic quantum theory, and great familiarity of the sub-atomic zoo and quantum number bookkeeping.

The volume has occasional errors, like reversing the assignment of the Kayon |Ks> and |KL> mixed states to the symmetric (should be anti-) and antisymmetric (should be sym.) combination of K0 and anti-K0. The math is right, but the explication in the text is wrong. Similar small errors popped up throughout the text, which was annoying in a 3rd edition.

The authors do give a very good overview of (most) possible prior and new versions of the standard model, but for an edition published late in 2000 I expected a lot more about adaptions that accounted well for neutrino mass. There is some there, just not as much as I'd like. I'm hoping in the 4th edition that there will be more discussion on the connundrum of the weak force's preference for left-handed chirality (all the more bizzare now that neutrinos are now thought to have mass). It will be several years before anyone publishes a successor text, since theorizing is still underway, and most particle physicists will be inclined to save their ink until after they've seen results from CERN's new Large Hadron Collider (LHC), to startup in 2007. I reckon that research and textbook writing delays will keep this book current until at least 2009.

The text occasionally has superb, succinct explanations of problems and motivation, but is given to long mathematical digressions into admittedly important crossection derivations. I wanted more chit-chat with my math. It also made disturbingly abrupt jumps in subject, however, the line of reasoning is very orderly, so it's possible to catch up with the authors. The technical English did bother me: being able to read mathematical German helped me a lot to recognize "what they really meant", since the English translation occasionally uses the wrong word, or a term depricated in physicist-English. It looks to me like it could benefit from some smoothing out (1) by a single physicist adding more bridge text between sections and (2) technical editing by a native English speaker, to tidy up awkward idiom. On the other hand, if you just want the straight scoop, and can pull it out of the math with a minimum of coddling and survive an occaional simple mistake, this book is for you.

It would be nice if there were more diagrams, but on the whole, the number of diagrams and pictures is adequate. A few more would make the math sing.

There are occasional biographical notes, which are nice, and the authors give sufficient historical background for the theory, which is good, but best of all is that they do not use "the historical approach" to particle physics. Thank you! The weak interaction is desribed in stages of increasing complexity from minimum adequate to possible next version(s). By coincidence, it's mostly in historical order, but they don't waste your time with no longer relevant background. That was excellent.

weak interaction and unified theory........2000-02-18

this volume is for advanced learner who has already has a background in quantum mechanics. this volume covers weak interaction. another volume quantum chromodynamics covers strong interaction. weak interaction is essential knowledge for starting research in elementary particle physics. it is also a necessary background for strings theory.

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