The geometry of physics : an introduction
Theodore Frankel.
Rev. ed.
Cambridge : Cambridge University Press, 2001, ©1997.
xxiv, 666 págs. : ilustraciones ; 26 cm.
ISBN: 0521387531 (pbk), 052138334X
Contiene correcciones a la ed. de 1997, y un nuevo apéndice.
Incluye referencias bibliográficas (p. 651-653) e índice.
Reseña: MathSciNet, 98h:58001
Contenido
- Part 1. Manifolds, tensors and exterior forms: 1. Manifolds and vector fields
- 2. Tensors and exterior forms
- 3. Integration of differential forms
- 4. The Lie derivative
- 5. The Poincaré lemma and potentials
- 6. Holonomic and nonholonomic constraints.
- Part 2. Geometry and topology: 7. $R3$ and Minkowski space
- 8. The geometry of surfaces in $R3$
- 9. Covariant differentiation and curvature
- 10. Geodesics
- 11. Relativity, tensors, and curvature
- 12. Curvature and topology: Synge's theorem
- 13. Betti numbers and de Rham's theorem
- 14. Harmonic forms.
- Part 3. Lie groups, bundles and Chern forms: 15. Lie groups
- 16. Vector bundles in geometry and physics
- 17. Fiber bundles, Gauss-Bonnet, and topological quantization
- 18. Connections and associated bundles
- 19. The Dirac equation
- 20. Yang-Mills fields
- 21. Betti numbers and covering spaces
- 22. Chern forms and homotopy groups.
- Appendix A. Forms in continuum mechanics
- Appendix B. Harmonic chains and Kirchhoff's circuit laws.
