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:
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.
Book Description
This collection of review lectures on topics in theoretical high energy physics has few rivals for clarity of exposition and depth of insight. Delivered over the past two decades at the International School of Subnuclear Physics in Erice, Sicily, the lectures help to organize and explain material that a the time existed in a confused state, scattered in the literature. At the time they were given they spread new ideas throughout the physics community and proved very popular as introductions to topics at the frontiers of research.
Customer Reviews:
A wonderful book to supplement one's QFT knowledge.......2003-08-04
This 400-page book contains eight lectures of varying length (some are quite long). The first two are not very useful, but the remainder of the book is wonderful. It covers topics like scale invariance, Callan-Symanzik (RG) equations, renormalization theory (Hepp's theorem), spontaneously broken symmetries, classical and quantum solitons, instantons (in QM and in gauge theories), and 1/N expansion. These are all useful topics and must be understood by those in the field, and yet not all of them are covered by ordinary quantum field theory books like Peskin & Schroeder. The style is very friendly and readable and includes a lot of endnotes, appendices, and references. This book does not "read" like Peskin/Schroeder or Weinberg or Itzykson/Zuber; those books don't read. This one does. The equations are easy to follow and this book showcases the strength of Coleman's pedagogical style. In fact I can vouch that the tone and content of these lectures serves as a close substitue for Coleman's lectures themselves. The topics were all basically developed in the 1970s, and were themselves all quite hot research areas before supersymmetry and string theory revolutionized high-energy physics. However, the majority of this book is not an anachronism -- the renormalization group, spontaneously broken symmetries, solitons, instantons, and 1/N expansion all pervade modern physics.
A Classic.......2003-05-17
Coleman is one of the best field theorists and a great lecturer. His style in both research and lectures can be summarized as "turning obvious into trivial". Every topic is presented in the simplest possible way without loss of deep insights, which makes the book extremely comprehensible. The chapter on instantons is absolutely classic.
unconventional QFT book.......2000-04-13
Many physicists say that Coleman is one of the great field theoriest in time. This is the collection of what he had lectured. Each chapter has own its importance. The advantage of the book is that he avoided the mathematical complication to explain the real physics. It is very unique feature in the QFT books. So you can get the concept of field theory without mathematical jargon which most students hate.
Book Description
Quantum Mechanics (Symmetries) deals with a particularly appealing and successful concept in advanced quantum mechanics. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry, and the general theory of Lie groups. The isospin group, hypercharge, SU(3) and their applications are all dealt with in depth before chapters on charm, SU(4), and dynamical symmetries lead to the frontiers of research in particle physics. This unique text comprises more than 120 detailed, worked examples and problems.As the third reprint of the second edition, this book has been revised to bring the text up to date.
Customer Reviews:
FIRST read a book in Lie groups.......2003-08-15
Book: Quantum Mechanics - Symmetries, 2nd edition, 15 chapters, 496 pages
Scope of the book: applications of group theory in elementary particle physic (no field theory!)
Reader: PhD student in physics, I am a beginner in that area, this is my first book in symmetries and Lie groups.
My evaluation:
The math sections in the book give u some basic notion of Lie groups but are NOT sufficient to fully understand the logic behind the scene everywhere. My advice is to read some good book in Lie groups in advance.
The strongest feature of the book is its richnes of examples and solved exercises both in group theory and in its application to particle physics. You can learn a lot of analytical 'tricks' from the solutions.
At the same time the text is full of small errors (signs, indeces, equation numbers, misprints). They are easy to detect and fun to debug and keep you concentrated while debugging.
My main objection is that very often the logic in the text remains hidden, broken or fuzzy. Sometimes they prove some statement but at the end you can't tell what was actually proven or under what conditions that proof is valid, what facts it is derived from, does it rely on implicit assumptions or it's generaly true. As a consequence of that you are not sure if you can apply the statement for a situation that is not exactly the one discussed in the book. Sometimes it's hard to tell if they are talking about a necessary of sufficient condition or both. Or they, having something in mind that you don't know about, make some sudden assumption and you wonder why. Some concepts are not defined sharply from the begining but instead the authors use fussy definitions and define them much later (example: tensor product of multiplets and its reduction is defined understandably in chapter 10 but is used all the time before that). The explanations of the algebra in the examples and exercises is also not the best since in many cases I see a more logical, organized and understandable way to explain it to the reader. Also in some cases the book gives just the algebra without giving the reader the more fundamental cause for some fact(example: in exercise 8.3 page 255 they have two matrices connected by a similarity transformation, they prove with some algebra that the eigenvalues remain the same but don't tell you that's always the case with similarity transformations).
To my opinion the authors have to a lot of work to do to make the logic fully explicit and understandable to the reader everywhere in the text. Without that, the book can be regarded as a nice collection of solved examples and exercises in group theory and particle physics.
I give that book 3 out of 5 stars and hope that the other volumes of the sequence don't have that flaw.
Contents of the book:
chap1: symmetries in classical physics, Noether's theorem, symmetries in quantum mechanics and their generators: momentum, angular momentum, energy and spin operators
chap2: angular momentum algebra; irreducible representations of SO(3); addition of angular momenta; Clebsh-Gordon coefficients
chap3: Lie groups, generators, Lie algebra; Casimir operators and Racah theorem; multiplets;
chap4: enumeration of the multiplets through eigenvalues of Casimir operators; energy degeneracy within a multiplet; two or more commuting symmety groups
chap5: neutron, proton doublet; isospin SU(2) symmetry; pion triplet; adjoint representation of Lie algebra
chap6: charge Q; hypercharge Y; baryons, antibaryons, baryon resonances; T3-Y diagrams;
chap7: U(n) and SU(n) groups; generators, Lie algebra of SU(3); subalgebras of SU(3) and shift operators; dimensions of SU(3) multiplets D(p,q);
chap8: smallest non-trivial representations of SU(3), quarks; meson multiplets; tensor product of multiplets and their reduction; Gell-Mann-Okubo mass formula; quark models with spin added, SU(6); wave functions construction, proton, neutron, baryon decuplet, baryon octet; mass formula in SU(6);
chap9: permutation group Sn, identical particles; Young diagrams; dimensions of irreducible Sn representations; connection to SU(n) multiplets; dimensions of SU(n); decompositions of SU(n) multiplet into SU(n-1) multiplets; decomposition of tensor product of multiplets with Young diagrams;
chap10: group characters; schur first and second lemma; orthogonality relations of characters of discrete finite groups; reduction of reducible representations; continuous, compact groups, group integration; integration over unitary groups; group characters of U(n); quark-gluon plasma example;
chap11: charm, SU(4), group generators; smallest non-trivial representations of SU(4), [4] and [4bar]; decomposition of tensor products of SU(4) multiplets; OZI rule for suppressing reactions; meson and baryon multiplets, SU(3) content; potential model of charmonium;SU(4)[with spin SU(8)] mass formula;
chap12: weight operators, standard Cartan-Weyl basis of a semi-simple Lie algebra; root vectors; graphic representations of root vectors and Lie algebras; simple roots and Dynkin diagrams;
chap13: space reflection (parity); time reversal; antilinear operators, complex conjugate operator K, antiunitary operator; general form of time reversal operator in coordinate representation for particle with spin;
chap14: classical hygrogen atom constants of motion: energy, angular momentum, Runge-Lenz vector; corresponding quantum constants of motion (operators), their algebra and group SO(4)- dynamical symmetry; decoupling of the SO(4) algebra into two SO(3) algebras and determination of the energy eigenvalues (Pauli method i guess); classical and quantum isotropic oscillator;
chap15: compact and noncompact Lie groups; group SU(p,q); group SO(p,q); generators of SO(2,1), infinitesimal operators, Casimir operators; non-compactness of SO(2,1) and its infinite dimensional irreducible unitary representations; application of SO(2,1) representations to scattering problems;
Book Description
Quantum Mechanics - Symmetries deals with a particularly appealing and successful concept in advanced quantum mechanics. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry, and the general theory of Lie groups. The isospin group, hypercharge, SU(3), and their applications are all dealt with in depth before chapters on charm, SU(4), and dynamical symmetries lead to the frontiers of research in particle physics. This unique text comprises more than 120 detailed, worked examples and problems. This second edition has been corrected and is presented in both a new attractive cover and a new format. In addition, some new examples and exercises have been included.
Customer Reviews:
A great companion book for learning Group Therory in Quantum Mechanics.......2007-07-10
When learning Quantum Mechanics (QM) you sooner or later just have to learn Group Theory.
There is no escape. The more advanced QM the more Group Theory there will be.
This book is "Group Theory in Action"!
However, my experience is that it is practically impossible to fully appreciate the ideas
of Group Theory from any physics text, including this one - even though it's entirely devoted
to the subject.
If you are new to the subject of groups, my advice is this:
1.) Read first an elementary text on Finite Groups.
Chapter 10 in the book Mathematics of Classical and Quantum Physics will do the job nicely and,
besides, you will own a book that covers a lot of the mathematics of QM.
2.) Read Greiners book in conjunction with a book on Matrix Lie Groups and Representation Theory.
The limitation to Matrix Lie Groups as opposed to General Lie Groups) is in the context of Greiners
book not a limitation at all. I strongly recommend the text Lie Groups, Lie Algebras, and Representations: An Elementary Introduction.
If you buy a more advanced text there will be prerequisites such as knowledge of Manifold Theory.
3.) Be aware of the following traps:
i.) As other reviewers have pointed out there are many small errors in the book, mostly typos.
There are also some bigger errors. For instance, the groups SU(2) and SO(3) are NOT isomorphic
as is stated in several places. (There is a 2:1 correspondence, i.e. a homomorphism and their
respective algebras are isomorphic.)
ii.) The book is not well organized in the sense that methods and concepts are used long before
they are properly defined. This is precicely why you should have a companion math text to go along
with it.
iii.) There is a constant change of notation in that quantities are defined in one way and given
a name and then, in the next paragraph a new name is introduced for a quantity that differs only
by a constant factor from the previous definition. This goes on and on and on and will be
confusing at first.
iv.) As in most physics texts there is a constant confusion as to what is what.
Groups and their respective Algebras are given the same name. One has to extract from the context what is meant.
Representations of groups and algebras, i.e. matrices (operators in the vector spaces of QM),
are confused with the invariant irreducible subspaces of the vector spaces on which the representations act.
This is something one has to get used to. It is the same in most physics texts and even in some math texts.
/********************/
Apart from these flaws, the book is fantastic. Just as it is hard to learn Group Theory from a
physics text alone, it's quite hard to learn Group Theory from a math text alone because typically,
there are very few solved problems to see the theory in action.
Therefore I recommend this book for students of mathematics as well as physics.
read a Lie groups math book FIRST.......2003-08-25
Book: Quantum Mechanics - Symmetries, 2nd edition, 15 chapters, 496 pages
Scope of the book: applications of group theory in elementary particle physic (no field theory!)
Reader: PhD student in physics, I am a beginner in that area, this is my first book in symmetries and Lie groups.
My evaluation:
The math sections in the book give u some basic notion of Lie groups but are NOT sufficient to fully understand the logic behind the scene everywhere. My advice is to read some good book in Lie groups in advance.
The strongest feature of the book is its richnes of examples and solved exercises both in group theory and in its application to particle physics. You can learn a lot of analytical 'tricks' from the solutions.
At the same time the text is full of small errors (signs, indexes, equation numbers, misprints). They are easy to detect and fun to debug and keep you concentrated while debugging.
My main objection is that very often the logic in the text remains hidden, broken or fuzzy. Sometimes they prove some statement but at the end you can't tell what was actually proven or under what conditions that proof is valid, what facts it is derived from, does it rely on implicit assumptions or it's generaly true. As a consequence of that you are not sure if you can apply the statement for a situation that is not exactly the one discussed in the book. Sometimes it's hard to tell if they are talking about a necessary of sufficient condition or both. Or they, having something in mind that you don't know about, make some sudden assumption and you wonder why (example: equation (13.3) on page 442 assumes that the parity transformed wave function is proportional to the old one. why? cause they assume implicitly without stating it that parity commutes with the Hamiltonian, hence they have common eigenfunctions). Some concepts are not defined sharply from the begining but instead the authors use fussy definitions and define them much later (example: tensor product of multiplets and its reduction is defined understandably in chapter 10 but is used all the time before that). The explanations of the algebra in the examples and exercises is also not the best since in many cases I see a more logical, organized and understandable way to explain it to the reader. Also in some cases the book gives just the algebra without giving the reader the more fundamental cause for some fact(example: in exercise 8.3 page 255 they have two matrices connected by a similarity transformation, they prove with some algebra that the eigenvalues remain the same but don't tell you that's always the case with similarity transformations).
To my opinion the authors have to a lot of work to do to make the logic structure of the text (the connections between different statements,the difference between assumptions and derivable facts) fully explicit and understandable to the reader everywhere in the text. Without that, the book can be regarded as a nice collection of solved examples and exercises in group theory and particle physics.
I give that book 3 out of 5 stars and hope that the other volumes of the sequence don't have that flaw.
Contents of the book:
chap1: symmetries in classical physics, Noether's theorem, symmetries in quantum mechanics and their generators: momentum, angular momentum, energy and spin operators
chap2: angular momentum algebra; irreducible representations of SO(3); addition of angular momenta; Clebsh-Gordon coefficients
chap3: Lie groups, generators, Lie algebra; Casimir operators and Racah theorem; multiplets;
chap4: enumeration of the multiplets through eigenvalues of Casimir operators; energy degeneracy within a multiplet; two or more commuting symmety groups
chap5: neutron, proton doublet; isospin SU(2) symmetry; pion triplet; adjoint representation of Lie algebra
chap6: charge Q; hypercharge Y; baryons, antibaryons, baryon resonances; T3-Y diagrams;
chap7: U(n) and SU(n) groups; generators, Lie algebra of SU(3); subalgebras of SU(3) and shift operators; dimensions of SU(3) multiplets D(p,q);
chap8: smallest non-trivial representations of SU(3), quarks; meson multiplets; tensor product of multiplets and their reduction; Gell-Mann-Okubo mass formula; quark models with spin added, SU(6); wave functions construction, proton, neutron, baryon decuplet, baryon octet; mass formula in SU(6);
chap9: permutation group Sn, identical particles; Young diagrams; dimensions of irreducible Sn representations; connection to SU(n) multiplets; dimensions of SU(n); decompositions of SU(n) multiplet into SU(n-1) multiplets; decomposition of tensor product of multiplets with Young diagrams;
chap10: group characters; schur first and second lemma; orthogonality relations of characters of discrete finite groups; reduction of reducible representations; continuous, compact groups, group integration; integration over unitary groups; group characters of U(n); quark-gluon plasma example;
chap11: charm, SU(4), group generators; smallest non-trivial representations of SU(4), [4] and [4bar]; decomposition of tensor products of SU(4) multiplets; OZI rule for suppressing reactions; meson and baryon multiplets, SU(3) content; potential model of charmonium;SU(4)[with spin SU(8)] mass formula;
chap12: weight operators, standard Cartan-Weyl basis of a semi-simple Lie algebra; root vectors; graphic representations of root vectors and Lie algebras; simple roots and Dynkin diagrams;
chap13: space reflection (parity); time reversal; antilinear operators, complex conjugate operator K, antiunitary operator; general form of time reversal operator in coordinate representation for particle with spin;
chap14: classical hygrogen atom constants of motion: energy, angular momentum, Runge-Lenz vector; corresponding quantum constants of motion (operators), their algebra and group SO(4)- dynamical symmetry; decoupling of the SO(4) algebra into two SO(3) algebras and determination of the energy eigenvalues (Pauli method i guess); classical and quantum isotropic oscillator;
chap15: compact and noncompact Lie groups; group SU(p,q); group SO(p,q); generators of SO(2,1), infinitesimal operators, Casimir operators; non-compactness of SO(2,1) and its infinite dimensional irreducible unitary representations; application of SO(2,1) representations to scattering problems;
quantum mechanics symmetries.......2000-07-27
This is the most stupid book that I have ever seen. The main concepts of Elementary Particles Theory are introduced before the Quantum Field Theory has been developed. Without knowing Dirac's equation how on the Earth is possible to grasp the intricasies of Modern Physics? Lee groups are not introduces properly either -- the level of mathematical discussion is very low. For all of you who wants to use comprehensive series on Modern Physics I recommend the old ones by Landau and Lifshitz.
QM for advanced larner........2000-02-22
Probably for most of the people it is better to start QM with easier books, e.g., Landou. Greiner's physics series are little more sophisticated, and may be difficult for someone with poor math background. For someone who has strong math background, Greiner's books are fun to read even without any physics background. With your strong math background, you can learn a lot out of this text.
full of useful mathematical tools........2000-02-20
this volume is not only useful for understanding non-relativistic quantum mechanics but also it is filled with mathematical tools that is useful in many science and engineering analysis. symmetry of the operators plays always an important role in simplifying the analysis of formidable coupled equations. i found this volume very useful in many ways.
Book Description
The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, aimed at undergraduate or graduate level students (depending on the college or university), concentrates on how to make predictions about the numbers of each kind of basic state of a quantum system from only two ingredients: the symmetry and the linear model of quantum mechanics. This method, involving the mathematical area of representation theory or group theory, combines three core mathematical subjects, namely, linear algebra, analysis and abstract algebra. Wide applications of this method occur in crystallography, atomic structure, classification of manifolds with symmetry, and other areas.
The topics unfold systematically, introducing the reader first to an important example of a quantum system with symmetry, the single electron in a hydrogen atom. Then the reader is given just enough mathematical tools to make predictions about the numbers of each kind of electronic orbital based solely on the physical spherical symmetry of the hydrogen atom. The final chapters address the related ideas of quantum spin, measurement and entanglement.
This user-friendly exposition, driven by numerous examples and exercises, requires a solid background in calculus and familiarity with either linear algebra or advanced quantum mechanics.
Linearity, Symmetry, and Prediction in the Hydrogen Atom will benefit students in mathematics, physics and chemistry, as well as a literate general readership.
A separate solutions manual is available to instructors.
Customer Reviews:
Well done.......2007-05-03
I bought this book at the Stanford bookstore a few days ago because it so closely matched what I was thinking of trying to understand myself, namely, how hard is it to go from the basic principles of quantum mechanics and recover experimental results about atoms. Well, the simplest atom is the hydrogen atom, and this book does the all the math associated with the s-shells, p-shells, energy levels, and so on, and it does so without bringing in extra physics or chemistry that a person is supposed to take on faith. If you're a mathematician who already knows some group representation theory (through Lie algebras, say), this book gives a particularly rapid path to understanding why the physicists find it so useful!
A joyful, illuminating book.......2006-06-03
Although I've taught quantum mechanics many times, I am learning a great deal from this splendid book. I much admire the care and consideration Singer has devoted to helping readers comprehend and enjoy fascinating, fundamental material. I hope she writes more such exceptional, mind-opening books! Dudley Herschbach, Prof. of Chemistry Harvard & Prof. of Physics, Texas A & M Univ.
Average customer rating:
- Emphasis here is on symmetries.
- A superb book
- Very good introduction to Lagrangian mechanics.
- An excellent readable introduction to Lagrangians in physics
|
Lagrangian Interaction: Introduction To Relativistic Symmetry In Electrodynamics And Gravitation
Doughty
Manufacturer: Westview Press
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Thermal Physics: Entropy and Free Energies
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The Classical Theory of Fields, Fourth Edition: Volume 2 (Course of Theoretical Physics Series)
ASIN: 0201416255 |
Customer Reviews:
Emphasis here is on symmetries........2006-10-31
I was expecting something along the lines of an updated Lanczos (The Variational Principles of Mechanics). But the emphasis here is very much on relativistic symmetries. Actually the book reminds me somewhat of Penrose's _Road to Reality_ and -- perhaps a better comparison -- Longair's _Theoretical Concepts in Physics_, with a mix of popular and semi-popular exposition, historical background, and more detailed mathematical exposition, but with a focus on relativistic symmetry (which still allows for a pretty wide-ranging number of topics in physics).
One complaint: the paper, printing and artwork are rather poor for a $45 paperback. Oxford and Cambridge Press, for example, produce much higher quality paperbacks in this price range. I've knocked off a star for that.
A superb book.......2001-10-24
This is work is comprehensive, easy to follow, and well-formatted. It is an excellent introduction to the action principle. It also serves as a great primer for the mathematics of special relativity, 4-vectors, vector fields and tensors. It is a shame that it doesn't go very far into GR (from the least action perspective) though.
Very good introduction to Lagrangian mechanics........1998-06-19
I highly recommend this book to undergraduate and graduate students in physics and astrophysics. It's clearly written, with a very modern approach (and book design!).
An excellent readable introduction to Lagrangians in physics.......1998-05-27
This is an excellent book. It is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity.
Book Description
Symmetries in Quantum Mechanics: From Angular Momentum to Supersymmetry (PBK) provides a thorough, didactic exposition of the role of symmetry, particularly rotational symmetry, in quantum mechanics. The bulk of the book covers the description of rotations (geometrically and group-theoretically) and their representations, and the quantum theory of angular momentum. Later chapters introduce more advanced topics such as relativistic theory, supersymmetry, anyons, fractional spin, and statistics. With clear, in-depth explanations, the book is ideal for use as a course text for postgraduate and advanced undergraduate students in physics and those specializing in theoretical physics. It is also useful for researchers looking for an accessible introduction to this important area of quantum theory.
Customer Reviews:
Excellent introduction to Angular Momentum in QM.......2000-03-29
I found this book to be very helpful in gaining a deeper understanding of the role of angular momentum in quantum mechanics. It was also a good introduction to Lie groups and Lie algebras for someone whos background is in physics and not math. I've found the book to be an invaluable reference!
Average customer rating:
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Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems
William J. Thompson
Manufacturer: Wiley-Interscience
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ASIN: 047155264X |
Book Description
Develops angular momentum theory in a pedagogically consistent way, starting from the geometrical concept of rotational invariance. Uses modern notation and terminology in an algebraic approach to derivations. Each chapter includes examples of applications of angular momentum theory to subjects of current interest and to demonstrate the connections between various scientific fields which are provided through rotations. Includes Mathematica and C language programs.
Customer Reviews:
A refreshing book.......2000-06-16
This book provides a pleasant alternative to the more classical books by Edmonds, Brink and Satchler or Rose: it's much more fun! The large number of illustrations (127) helps the reader to grasp some fundamental aspects of angular momentum. All the basics of this subject are covered. The reading is facilitated by the fact that many proofs are left as exercices (and can be found in more classical treatments of the subject). For those who have Mathematica at their disposal, the programs that are included in the book can fruitfully by used for further exploration of the properties of angular momentum.
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Fields, Symmetries, and Quarks
Ulrich Mosel
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover
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ASIN: 3540652353 |
Book Description
This textbook covers elements of quantum field theory, symmetry principles, gauge field theories and phenomenological descriptions of hadrons, with special emphasis on topics relevant to hadron and nuclear physics. Written at an introductory level, it is aimed at nuclear physicists in general and experimentalists in particular who need a working knowledge of field theory, symmetry principles of elementary particles and their interactions and the quark structure of hadrons. It will also be of benefit to graduate students who need an understanding of the basics of these topics for their work in other fields.
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Supersymmetry In Quantum and Classical Mechanics
Bijan Kumar Bagchi
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover
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ASIN: 1584881976 |
Book Description
Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods. Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.
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