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.
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.
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.
Inhaltsangabe
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.
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.
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