Differential Geometry in Physics 1st Edition by Gabriel Lugo ISBN 1469669242 9781469669243

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ISBN 10: 1469669242 
ISBN 13: 9781469669243
Author: Gabriel Lugo

Differential Geometry in Physics is a treatment of the mathematical foundations of the theory of general relativity and gauge theory of quantum fields. The material is intended to help bridge the gap that often exists between theoretical physics and applied mathematics.

The approach is to carve an optimal path to learning this challenging field by appealing to the much more accessible theory of curves and surfaces. The transition from classical differential geometry as developed by Gauss, Riemann and other giants, to the modern approach, is facilitated by a very intuitive approach that sacrifices some mathematical rigor for the sake of understanding the physics. The book features numerous examples of beautiful curves and surfaces often reflected in nature, plus more advanced computations of trajectory of particles in black holes. Also embedded in the later chapters is a detailed description of the famous Dirac monopole and instantons.

Differential Geometry in Physics 1st Table of contents:

1. The concept of a manifold

2. Vector and tensor fields

3. Mappings of tensors induced by mappings of manifolds

4. Lie derivative

5. Exterior algebra

6. Differential calculus of forms

7. Integral calculus of forms

8. Particular cases and applications of Stokes’s Theorem

9. Poincaré Lemma and cohomologies

10. Lie Groups – basic facts

11. Differential geometry of Lie Groups

12. Representations of Lie Groups and Lie Algebras

13. Actions of Lie Groups and Lie Algebras on manifolds

14. Hamiltonian mechanics and symplectic manifolds

15. Parallel transport and linear connection on M

16. Field theory and the language of forms

17. Differential geometry on TM and T*M

18. Hamiltonian and Lagrangian equations

19. Linear connection and the frame bundle

20. Connection on a principal G‑bundle

21. Gauge theories and connections

22. Spinor fields and Dirac operator

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Tags: Gabriel Lugo, Differential Geometry, Physics