Résumé
Aimed at instructors and graduate students, this book provides a detailed introduction to the modern applications of groups, algebras, and topology in physics. Adopting an example-based approach, it contains worked examples throughout and over 300 problems of varying complexity. Separate instructor and student solutions manuals are available.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 Poincare 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. Poincare 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.Mike Guidry is Professor in Physics and Astronomy at the University of Tennessee. He is the author of more than 125 journal articles and six published textbooks. He has been the Lead Educational Technology Developer for several major college textbooks in introductory physics, astronomy, biology, genetics, and microbiology. During his career, he has won multiple teaching awards and has taken the lead in a variety of science outreach initiatives. Yang Sun gained his Ph.D. at the Technical University of Munich and has many years of experience teaching undergraduate courses, ranging from introductory physics to quantum mechanics. He is the author of more than 250 journal articles, mainly in the field of nuclear many-body theory, but also in other correlated fermionic systems. He was awarded the Wu Youxun Prize by the Chinese Physical Society for his research achievements.
