Symmetry, broken symmetry, and topology in modern physics : a first course

著者

    • Guidry, Mike
    • Sun, Yang

書誌事項

Symmetry, broken symmetry, and topology in modern physics : a first course

Mike Guidry, Yang Sun

Cambridge University Press, 2022

  • : hardback

大学図書館所蔵 件 / 全15件

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注記

Includes bibliographical references (p. 609-616) and index

内容説明・目次

内容説明

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.

目次

  • 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.

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