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Quantum Theory, Groups and Representations

An Introduction

  • Peter Woit

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Peter Woit
    Pages 1-14
  3. Peter Woit
    Pages 27-37
  4. Peter Woit
    Pages 103-124
  5. Peter Woit
    Pages 139-147
  6. Peter Woit
    Pages 149-164
  7. Peter Woit
    Pages 165-180
  8. Peter Woit
    Pages 229-236
  9. Peter Woit
    Pages 237-243
  10. Peter Woit
    Pages 259-273
  11. Peter Woit
    Pages 275-285
  12. Peter Woit
    Pages 287-298
  13. Peter Woit
    Pages 341-356
  14. Peter Woit
    Pages 357-363
  15. Peter Woit
    Pages 365-372
  16. Peter Woit
    Pages 373-381
  17. Peter Woit
    Pages 395-410
  18. Peter Woit
    Pages 413-420
  19. Peter Woit
    Pages 433-445
  20. Peter Woit
    Pages 503-513
  21. Peter Woit
    Pages 515-525
  22. Peter Woit
    Pages 621-626
  23. Peter Woit
    Pages 627-629

About this book

Introduction

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.

Keywords

Lie algebras Lie groups quantization quantum fields quantum mechanics representation theory Standard Model of particle physics unitary group representations two-state systems Lie algebra representations rotation and spin groups momentum and free particle fourier analysis and free particle Schroedinger representation Heisenberg group Poisson bracket and symplectic geometry Hamiltonian vector fields quantum free particle metaplectic representation Fermionic oscillator

Authors and affiliations

  • Peter Woit
    • 1
  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA

Bibliographic information