Symmetry, Broken Symmetry, and Topology in Modern Physics
A First Course

A pedagogical introduction to the modern applications of groups, algebras, and topology for undergraduate and graduate students in physics.

Mike Guidry (Author), Yang Sun (Author)

9781316518618, Cambridge University Press

Hardback, published 31 March 2022

664 pages
25.3 x 19.4 x 3.3 cm, 1.56 kg

'The whole of theoretical physics, and our general picture of the world, are based on symmetries. This book is devoted to symmetries and their manifestations in nature, and it allows students to develop a theoretical and experimental understanding of the fundamental properties of the Universe. This path is carefully paved by the authors.' Professor Vladimir Zelevinsky, Michigan State University

Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.

Preface
Part I. Symmetry Groups and Algebras: 1. Introduction
2. Some properties of groups
3. Introduction to lie groups
4. Permutation groups
5. Electrons on periodic lattices
6. The rotation group
7. Classification of lie algebras
8. Unitary and special unitary groups
9. SU(3) flavor symmetry
10. Harmonic oscillators and SU(3)
11. SU(3) matrix elements
12. Introduction to non-compact groups
13. The Lorentz group
14. Lorentz covariant fields
15. Poincaré invariance
16. Gauge invariance
Part II. Broken Symmetry: 17. Spontaneous symmetry breaking
18. The Higgs mechanism
19. The standard model
20. Dynamical symmetry
21. Generalized coherent states
22. Restoring symmetry by projection
23. Quantum phase transitions
Part III. Topology and Geometry: 24. Topology, manifolds, and metrics
25. Topological solitons
26. Geometry and gauge theories
27. Geometrical phases
28. Topology of the quantum Hall effect
29. Topological matter
Part IV. A Variety of Physical Applications: 30. Angular momentum recoupling
31. Nuclear fermion dynamical symmetry
32. Superconductivity and superfluidity
33. Current algebra
34. Grand unified theories
Appendix A. Second quantization
Appendix B. Natural units
Appendix C. Angular momentum tables
Appendix D. Lie algebras
References
Index.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Groups & group theory [PBG]