Physicist's geometry

Author: Theodore Frankel
Publisher:
Publish Date: 2005-04-01
Features: This book attempts to provide advanced knowledge of exterior differential forms, differential geometry, algebraic topology, differential topology, Lie groups, vector bundles, and Chern formulas, which are essential for a deeper understanding of classical physics, modern physics, and engineering. It includes discussions on analytical dynamics, fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, elasticity theory, the geometry and topology of Kirchhoff's circuit laws, soap films, special and general relativity, the Dirac operator and spinors, Yang-Mills gauge fields, the Aharonov-Bohm effect, Berry phase, instanton winding numbers, quarks, and the quark model for mesons. Before delving into the abstract concepts of differential geometry, geometric intuition is developed through an extensive introduction to the study of surfaces in ordinary space, making the book of interest to mathematics students as well. This book will be useful to graduate and advanced undergraduate students of physics, engineering, and mathematics, serving as a valuable self-study textbook. This second edition includes three new appendices: Appendix C, Symmetries, Quarks, and Meson Masses (which concludes with the famous Gell-Mann/Okubo mass formula); Appendix D, Representations and Hyperelastic Bodies; and Appendix E, Orbits and Morse-Bott Theory in Compact Lie Groups. Both Appendix C and D involve results from the theory of representations of compact Lie groups, which are developed here. Appendix E delves deeper into the geometry and topology of compact Lie groups.