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Author : D. J. Simms
Publisher : Springer
Page : 93 pages
File Size : 52,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540358299
Author : Peter Woit
Publisher : Springer
Page : 668 pages
File Size : 54,7 Mb
Release : 2017-11-01
Category : Science
ISBN : 9783319646121
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Author : Arnold Neumaier,Dennis Westra
Publisher : Unknown
Page : 500 pages
File Size : 46,6 Mb
Release : 2020-10-04
Category : Science
ISBN : 3110406101
Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 50,7 Mb
Release : 2013-06-19
Category : Science
ISBN : 9781461471165
Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Author : Yair Shapira
Publisher : Unknown
Page : 678 pages
File Size : 50,6 Mb
Release : 2021
Category : Mechanics
ISBN : 981124006X
Author : Jürgen Fuchs
Publisher : Cambridge University Press
Page : 452 pages
File Size : 45,7 Mb
Release : 1995-03-09
Category : Mathematics
ISBN : 052148412X
This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.
Author : George Lusztig
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 43,7 Mb
Release : 2010-10-27
Category : Mathematics
ISBN : 9780817647179
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 41,5 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780387782157
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).
Author : Robert Gilmore
Publisher : Cambridge University Press
Page : 5 pages
File Size : 49,5 Mb
Release : 2008-01-17
Category : Science
ISBN : 9781139469074
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
Author : Vladislav Kharchenko
Publisher : Springer
Page : 0 pages
File Size : 54,5 Mb
Release : 2015-12-25
Category : Mathematics
ISBN : 3319227033
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
Author : Robert Gilmore
Publisher : Courier Corporation
Page : 610 pages
File Size : 52,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131566
This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
Author : A. Zee
Publisher : Princeton University Press
Page : 632 pages
File Size : 47,8 Mb
Release : 2016-03-29
Category : Science
ISBN : 9781400881185
A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)
Author : Josi A. de Azcárraga,Josi M. Izquierdo
Publisher : Cambridge University Press
Page : 480 pages
File Size : 55,7 Mb
Release : 1998-08-06
Category : Mathematics
ISBN : 0521597005
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
Author : Robert Hermann
Publisher : Unknown
Page : 216 pages
File Size : 41,9 Mb
Release : 1966
Category : Lie groups
ISBN : STANFORD:36105031202687
Author : Ashok Das,Susumu Okubo
Publisher : Unknown
Page : 0 pages
File Size : 43,7 Mb
Release : 2014
Category : Group theory
ISBN : 9814603279
The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.
