5 edition of Quantum Groups and Their Applications in Physics found in the catalog.
January 1, 1996
by Ios Pr Inc
Written in English
|Contributions||Leonardo Castellani (Editor), Julius Wess (Editor), Societa Italiana Di Fisica (Corporate Author)|
|The Physical Object|
|Number of Pages||652|
The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. Abstract. This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of : L Castellani and J Wess.
This book is the fruit of for many years teaching the introduction to quan-tum mechanics to second-year students of physics at Oxford University. We have tried to convey to students that it is the use of probability amplitudes rather than probabilities that makes quantum mechanics the extraordinary. This is a course about groups and their representations, with an emphasis on topics arising in physical applications. This is a vast topic, with an unbelievably wide spectrum of applications to physics. I will cover basic de nitions and examples, and also illustrate these with more advanced applications. 2. Boundary Conditions.
According to Drinfeld, a quantum group is the same as a Hopf algebra. This includes as special cases, the algebra of regular functions on an algebraic group and the enveloping algebra of a semisimple Lie algebra. The qu- tum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in , or variations thereof. Quantum Theory, Groups and Representations: An Introduction Peter Woit Department of Mathematics, Columbia University [email protected]
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This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of by: 7.
This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest.
The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory. This book gives a comprehensive view of quantum groups and their applications.
The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Researchers in mathematics and theoretical physics will enjoy this by: In fact, such groups play a large Quantum Groups and Their Applications in Physics book in quantum mechanics and elementary particle physics, and some facts about them should be noted here.
Their representations share many of the properties of the representations of finite groups, but the methods of working with the groups is somewhat different. QUANTUM GROUPS AND THEIR APPLICATIONS IN NUCLEAR PHYSICS Dennis BONATSOS Institute of Nuclear Physics, N.C.S.R.
\Demokritos" GR Aghia Paraskevi, Attiki, Greece C. DASKALOYANNIS Department of Physics, Aristotle University of Thessaloniki GR Thessaloniki, Greece ABSTRACT. Get this from a library. Quantum groups and their applications in physics: Varenna on Lake Como, Villa Monastero, 28 June-8 July [Leonardo Castellani; Julius Wess; Società italiana di fisica.;].
Intuitive meaning. The discovery of quantum groups was quite unexpected since it was known for a long time that compact groups and semisimple Lie algebras are "rigid" objects, in other words, they cannot be "deformed". One of the ideas behind quantum groups is that if we consider a structure that is in a sense equivalent but larger, namely a group algebra or a universal enveloping algebra.
This book gives a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Researchers in mathematics and theoretical physics will enjoy this by: Publisher Summary.
This chapter describes the structure of the matrices for arbitrary finite r-transformations with their properties, and their wide-ranging applications to macroscopic and quantum properties of irreducible standard sets of arbitrary degree j can be derived by constructing such sets from the direct product of 2j identical standard sets of degree 1/2.
The theory of groups supplies vector spaces, quantum numbers, and matrix elements for quantum mechanics. This chapter discusses finite groups, in particular point groups and symmetric group.
The symmetric group is of central importance in the theory of systems with identical particles: electrons for atoms, molecules, and solids, nucleons for. There is a book titled "Group theory and Physics" by Sternberg that covers the basics, including crystal groups, Lie groups, representations.
I think it's a good introduction to the topic. To quote a review on Amazon (albeit the only one): "This book is an excellent introduction to the use of group theory in physics, especially in crystallography, special relativity and particle physics.
A classical reference, in particular for discrete groups and applications in quantum mechanics. • H. Weyl,“Quantum mechanics and group theory,” Z. Phys. 46 () 1. One of the original foundations of the use of symmetry in quantum mechanics • R. Cahn, “Semisimple Lie Algebras And Their Representations,” Menlo Park.
The majority of our loyal Quantum Physics Discussion Group Members are interested in the more substantive ideas of physics, both experimental and theoretical, and far less interested, if at all, in the "new-age," loosey- goosey, marginally speculative fantasy or "spiritual" thinking that sometimes, and maybe even too often, passes for science.
Title: Quantum Groups and Their Applications in Nuclear Physics. Authors: Dennis Bonatsos, Abstract: Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case.
After a self-contained introduction to the necessary mathematical Cited by: Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics.
No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail).Cited by: There is an ongoing effort trying to geometrize the notion of quantum groups (as stated at page $28$ of the paper of Maulik and Okounkov).
See the wonderful and exhaustive answer by Will Orrick. To learn quantum groups you will need some knowledge of physics (to have a motivation for the subject and maybe to get some intuition), Lie groups and.
This book is devoted to the consistent and systematic application of group theory to quantum mechanics. Beginning with a detailed introduction to the classical theory of groups, Dr. Weyl continues with an account of the fundamental results of quantum physics.
of the book is an overview of what the author calls quantum SL(2), which is an example of a Hopf algebra. Quantum Groups (Graduate Texts in Mathematics) Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in File Size: KB.
There is a good book by John F. Cornwell entitled Group Theory in Physics: An Introduction. This book is an abridged version of a book in two volumes by the same author, entitled Group Theory in Physics. A useful reference and a classic about grou.
This book describes the following topics: Relativistic wave equations, Groups and their representations, The Dirac equation, Vector fields and Maxwell equations, Classical lagrangian field theory, Quantization of field, Discrete symmetries, Path integrals and quantum mechanics, Feynman diagrams for scattering amplitudes, Scattering theory and.Algebra and Applications aims to publish well-written and carefully refereed monographs with up-to-date expositions of research in all fields of algebra, including its classical impact on commutative and noncommutative algebraic and differential geometry, K-theory and algebraic topology, and further applications in related domains, such as number theory, homotopy and (co)homology theory.Quantum groups with two parameters ; Quantum group theoretic proof of the addition formula for continuous q-Legendre polynomials ; q-special functions, a tutorial ; q-special functions and their occurrence in quantum groups ; Quantum flag and Schubert schemes