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

ISBN-13: 9781316518618 / Angielski / Twarda / 2022

China) Sun Yang (Shanghai Jiao Tong University

Opis

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

Recenzje

'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

Spis treści

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.