Book Description
This graduate-level text develops aspects of group theory most relevant to physics and chemistry and illustrates their applications to quantum mechanics: abstract group theory, theory of group representations, physical applications of group theory, full rotation group and angular momentum, quantum mechanics of atoms, molecular quantum mechanics, and solid-state theory. 1964 edition.
Customer Reviews:
Heavy on the Math . . ........2007-09-10
This book is an excellent reference for group theory. It gives you the detailed math behind group theory (which is great for me). It also gives you a brief introduction so you can work with molecular group theory. This was the recommended text in my chemical group theory class. It serves as a good mathematical reference. Also, see Cotton's group theory book, and Carters group theory book.
Good for the Undergrad Students........2007-08-27
This book has the advantage of applying group theory directly to solvable physical problems. In most areas of applied physics it is
very important to know the basics concepts of group theory, but
there is no need to have a deep knowledge as well as to know how to
proof all the main theorems. As an introductory course for undergrad
students this book is well recommended.
Most accessible of the useful physics texts.......2006-08-11
My background is that of theoretically inclined inorganic chemist and this review is intended for those with interests in inorganic and physical chemistry or solid-state chemistry/physics.
Tinkham's text is the first textbook one should go to for a reasonably rigorous introduction to the theory and use of group representations in physics and theoretical chemistry. Modern theoretical chemists should become familiar with all of this book, with the possible exception of the some of the material in Chapter 5 that will be applicable only to physicists (and not a lot of that, actually). The pervasiveness of band theory, even in general inorganic chemistry journals now, should convince chemists who teach this subject to include a lot of Chapter 8 (Solid-State Theory) and chemical theorists will even have to go beyond the symmorphic groups treated here.
The purely mathematical aspects of the subject are treated briefly, but much more completely, than "chemical group theory books" like Cotton's, for example. Naturally, this comes at a price of more mathematical abstractness, but that is unavoidable. These sections, like the rest of the book, are very well written.
Chapter 7, on applications to molecular quantum mechanics, is now quite dated. It was quite incomplete even when written, since it did not include any discussion of ligand-field theory. The effects of antisymmetric wavefunctions for electrons are touched on briefly in Chapter 5 (atoms), but are not adequately accounted for in discussion of molecules. (Incidentally, the failure to use Mulliken notation in molecular QM is an unfortunate annoyance.)
These objections aside, this book is an excellent buy for the price of a Dover edition. Indeed, if I'd included price in my rating, it would be 5 stars - easily!
A must for every grad student.......2005-12-27
I began reading this book having just finished a course on Abstract Algebra through my school's math department, and the semester before I took a graduate course on the exact subject.
After taking the math course, I was presented with group theory as if it were some muddled mix of facts, and the course came across as a poorly taught class on number theory. After reading just the first chapter of Tinkham's book, I developed a new, deeper understanding of group theory as a whole. For example, the way that Tinkham presents normal subgroups makes vastly more intuitive sense than the presentation I received in my math course.
The first two chapters alone are probably worth 80% of the book's sale price. The rest is made up entirely of the fact that the book does not piddle around with trivial examples, but genuinely frames quantum mechanics in the language of group theory, and the most important part is that Tinkham does it well.
This book, along with his book on superconductivity, are must-haves for any serious condensed matter person, and this book should be at least read (if not owned) by any physics grad student.
Group Theory and Quantum Mechanics.......2005-07-19
Both the content of the book and service of amazon are wonderful
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Symplectic Geometry and Quantum Mechanics (Operator Theory: Advances and Applications / Advances in Partial Differential Equations)
Maurice de Gosson
Manufacturer: Birkhäuser Basel
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Book Description
This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.
Book Description
This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.
Customer Reviews:
one the the most important work in quantum mechanics.......2006-02-22
It's a very important book, written by the father of group theory application in physics (with Wigner and Pauli), and one of the best mathematician of 20th century, Hermann Weyl. Everyone who wants study a deeper view of quantum mechanics, in his intrinsic mathematical formulation, should read this work. After a firt brief introduction to quantum theory, he passes to explain the theory of rapresentation of groups, and its physical application, like the rotation group, or Lorentz group, and finally the theory of simmetry. It's a fundamental book for a good understandig of the importance of simmetries in modern physics. Without any doubt one the the most important work in quantum mechanics.
Still a good book.......2003-02-27
Written in the early years of the quantum theory, the author of this book foresaw the importance of considering symmetry in physics, the use of which now pervades most of theoretical high energy physics. Indeed, with the advent of gauge theories, and their experimental validation, it is readily apparent that symmetry principles are here to stay, and are just not accidental curiosities. A reader of the book can still gain a lot from the perusal of this book, in spite of its date of publication and its somewhat antiquated notation. Older books also have the advantage of discussing the material more in-depth, and do not hesitate to use hand-waving geometrical pictures when appropriate. This approach results in greater insight into the subject, and when coupled with eventual mathematical rigor gives it a solid foundation. One example where the discussion is superior to modern texts is in the author's discussion of group characters and their application to irreducible representations and spectra in atomic systems.
The reader will no doubt probably want to couple the reading of this book with a more modern text so as to alleviate the notational oddities in this book. The author's presentation is clear enough though to make an appropriate translation to modern notation. The reader will then be well prepared to tackle more advanced material in mathematical and theoretical physics that make use of the group-theoretic constructions that take place in this book.
A wonderful book.......2001-11-08
This is my favorite introduction to quantum mechanics. It is a difficult book, because it is succinct, though clear, and reflects Weyl's powerful intellect and original approach at every step. Each page is a challenge, but worth the effort.
One of the two great classics on group theory in physics.......2001-02-18
The other one is Wigner's "Group Theory and Quantum Mechanics". As it is true of the other great books by Weyl, this is not an easy book, but it is, by all means, accessible. Don't try to read it in front of the TV set. Get pencil and paper, put yourself in a calm and contemplative mood and patiently read the words of the master. Hermann Weyl, one of the great minds of the 20th century, wrote this book with utmost care to make it self-contained. Sometimes you have to be deep in order to be brief, so the book requires some thought. But the main ideas are all there, and the connection of group theory with quantum mechanics has here its best treatment, in my humble opinion. But in less humble too: this was the only book concerning physics which Enrico Fermi read as a grown up. Once, Max Born had to write a synthetic exposition of Quantum Mechanics. After he finished it, he saw, for the first time, this book, and Weyl's synthesis of QM. He felt depressed by the superiority of Weyl's text. The book was originally written in German, but the translation is excellent, due to the great American cosmologist H. P. Robertson, of Robertson-Walker fame.
Classic from the early days of quantum mechanics.......2000-06-27
Although published by Dover in 1984, this book dates back to about 1930, when Weyl was the big proponent of group theory in quantum mechanics. Because of this date, much of what modern books on group theory would include, is absent from the book. It mainly discusses the permutation group. The book is, however, of historic interest, as Weyl (mathematician) tried to convince the physicists to exploit group theory - which even gave rise to some irritation ("group pest").
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:
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Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups (Lecture Notes in Physics , No 39)
Ludwig Pittner
Manufacturer: Springer
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Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.
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Conformal Field Theory and Topology
Toshitaki Kohno
Manufacturer: American Mathematical Society
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ASIN: 082182130X |
Book Description
Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariant for 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometry as well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds.
The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treats Chern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.
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Recommended Books
- History: Fiction or Science
- First Day in Grapes
- Birds of Prey: A Novel of Suspense
- Callahan's Lady
- Classical Dynamics of Particles and Systems
- Essentials of Computational Chemistry: Theories and Models
- Crazy Horse and Custer: The Parallel Lives of Two American Warriors
- Royal Arts of Africa, The: The Majesty of Form
- Autobiography of Dr Karl Ernest Von Baer
- A simplified manual of interesting California trees of forest, desert, and city: Both native and int
Introduction to Superconductivity: Second Edition (Dover Books on Physics)
Mathematical Foundations of Quantum Mechanics (Dover Books on Mathematics)
Lie Groups for Pedestrians
Lie Groups, Lie Algebras, and Some of Their Applications
Symmetry: An Introduction to Group Theory and Its Applications
