 Systematically emphasizes the role of Lie groups, Lie algebras, and their unitary representation theory in the foundations of quantum mechanics
 Introduces fundamental structures and concepts of representation theory in an elementary, physically relevant context
 Gives a careful treatment of the mathematical subtleties of quantum theory, without obscuring its global mathematical shape
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 About this Textbook

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 quantumtheoretical concepts and calculations.
 About the authors

Peter Woit is a Senior Lecturer of Mathematics at Columbia University. His general area of research interest is the relationship between mathematics, especially representation theory, and fundamental physics, especially quantum field theories like the Standard Model.
 Reviews

“The book presents a large variety of important subjects, including the basic principles of quantum mechanics … . This good book is recommended for mathematicians, physicists, philosophers of physics, researchers, and advanced students in mathematics and physics, as well as for readers with some elementary physics, multivariate calculus and linear algebra courses.” (Michael M. Dediu, Mathematical Reviews, June, 2018)
 Table of contents (49 chapters)


Introduction and Overview
Pages 114

The Group U(1) and its Representations
Pages 1526

Twostate Systems and SU(2)
Pages 2737

Linear Algebra Review, Unitary and Orthogonal Groups
Pages 3953

Lie Algebras and Lie Algebra Representations
Pages 5571

Table of contents (49 chapters)
 Download Preface 1 PDF (54.9 KB)
 Download Sample pages 2 PDF (240 KB)
 Download Table of contents PDF (567.3 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Quantum Theory, Groups and Representations
 Book Subtitle
 An Introduction
 Authors

 Peter Woit
 Copyright
 2017
 Publisher
 Springer International Publishing
 Copyright Holder
 Peter Woit
 eBook ISBN
 9783319646121
 DOI
 10.1007/9783319646121
 Hardcover ISBN
 9783319646107
 Softcover ISBN
 9783319878355
 Edition Number
 1
 Number of Pages
 XXII, 668
 Number of Illustrations
 27 b/w illustrations
 Topics