Mathematical Physics

Robert Geroch

Published by University of Chicago Press 1984

Mathematical Physics

Robert Geroch

In the series Chicago Lectures in Physics

https://doi.org/10.7208/9780226223063

Overview
Contents

About this book

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.

Author / Editor information

Robert Geroch is professor in the Departments of Physics and Mathematics and at the Enrico Fermi Institute at the University of Chicago.

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	v
1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2. Categories Requires Authentication Unlicensed Licensed Download PDF	3
3. The Category of Groups Requires Authentication Unlicensed Licensed Download PDF	16
4. Subgroups Requires Authentication Unlicensed Licensed Download PDF	24
5. Normal Subgroups Requires Authentication Unlicensed Licensed Download PDF	29
6. Homomorphisms Requires Authentication Unlicensed Licensed Download PDF	32
7. Direct Products and Sums of Groups Requires Authentication Unlicensed Licensed Download PDF	35
8. Relations Requires Authentication Unlicensed Licensed Download PDF	39
9. The Category of Vector Spaces Requires Authentication Unlicensed Licensed Download PDF	44
10. Subspaces Requires Authentication Unlicensed Licensed Download PDF	53
11. Linear Mappings; Direct Products and Sums Requires Authentication Unlicensed Licensed Download PDF	58
12. From Real to Complex Vector Spaces and Back Requires Authentication Unlicensed Licensed Download PDF	62
13. Duals Requires Authentication Unlicensed Licensed Download PDF	65
14. Multilinear Mappings; Tensor Products Requires Authentication Unlicensed Licensed Download PDF	71
15. Example: Minkowski Vector Space Requires Authentication Unlicensed Licensed Download PDF	79
16. Example: The Lorentz Group Requires Authentication Unlicensed Licensed Download PDF	87
17. Functors Requires Authentication Unlicensed Licensed Download PDF	90
18. The Category of Associative Algebras Requires Authentication Unlicensed Licensed Download PDF	97
19. The Category of Lie Algebras Requires Authentication Unlicensed Licensed Download PDF	104
20. Example: The Algebra of Observables Requires Authentication Unlicensed Licensed Download PDF	111
21. Example: Fock Vector Space Requires Authentication Unlicensed Licensed Download PDF	114
22. Representations: General Theory Requires Authentication Unlicensed Licensed Download PDF	120
23. Representations on Vector Spaces Requires Authentication Unlicensed Licensed Download PDF	125
24. The Algebraic Categories: Summary Requires Authentication Unlicensed Licensed Download PDF	132
25. Subsets and Mappings Requires Authentication Unlicensed Licensed Download PDF	134
26. Topological Spaces Requires Authentication Unlicensed Licensed Download PDF	136
27. Continuous Mappings Requires Authentication Unlicensed Licensed Download PDF	147
28. The Category of Topological Spaces Requires Authentication Unlicensed Licensed Download PDF	154
29. Nets Requires Authentication Unlicensed Licensed Download PDF	160
30. Compactness Requires Authentication Unlicensed Licensed Download PDF	165
31. The Compact-Open Topology Requires Authentication Unlicensed Licensed Download PDF	172
32. Connectedness Requires Authentication Unlicensed Licensed Download PDF	177
33. Example: Dynamical Systems Requires Authentication Unlicensed Licensed Download PDF	183
34. Homotopy Requires Authentication Unlicensed Licensed Download PDF	188
35. Homology Requires Authentication Unlicensed Licensed Download PDF	199
36. Homology: Relation to Homotopy Requires Authentication Unlicensed Licensed Download PDF	211
37. The Homology Functors Requires Authentication Unlicensed Licensed Download PDF	214
38. Uniform Spaces Requires Authentication Unlicensed Licensed Download PDF	217
39. The Completion of a Uniform Space Requires Authentication Unlicensed Licensed Download PDF	225
40. Topological Groups Requires Authentication Unlicensed Licensed Download PDF	234
41. Topological Vector Spaces Requires Authentication Unlicensed Licensed Download PDF	240
42. Categories: Summary Requires Authentication Unlicensed Licensed Download PDF	248
43. Measure Spaces Requires Authentication Unlicensed Licensed Download PDF	249
44. Constructing Measure Spaces Requires Authentication Unlicensed Licensed Download PDF	257
45. Measurable Functions Requires Authentication Unlicensed Licensed Download PDF	259
46. Integrals Requires Authentication Unlicensed Licensed Download PDF	262
47. Distributions Requires Authentication Unlicensed Licensed Download PDF	270
48. Hilbert Spaces Requires Authentication Unlicensed Licensed Download PDF	277
49. Bounded Operators Requires Authentication Unlicensed Licensed Download PDF	285
50. The Spectrum of a Bounded Operator Requires Authentication Unlicensed Licensed Download PDF	293
51. The Spectral Theorem: Finite-dimensional Case Requires Authentication Unlicensed Licensed Download PDF	302
52. Continuous Functions of a Hermitian Operator Requires Authentication Unlicensed Licensed Download PDF	306
53. Other Functions of a Hermitian Operator Requires Authentication Unlicensed Licensed Download PDF	311
54. The Spectral Theorem Requires Authentication Unlicensed Licensed Download PDF	319
55. Operators (Not Necessarily Bounded) Requires Authentication Unlicensed Licensed Download PDF	324
56. Self-Adjoint Operators Requires Authentication Unlicensed Licensed Download PDF	329
Index of Defined Terms Requires Authentication Unlicensed Licensed Download PDF	343

Language: English
Publisher: University of Chicago Press
Audience: Professional and scholarly;
Pages
- Main content: 358
Keywords: vectors; topology; physics; math; mathematics; hilbert space; mathematical structures; relativity; astrophysics; operators; spectral theorem; hermitian operator; bounded; topological groups; integrals; distribution; homology; functions; homotopy; connectedness; compactness; mappings; fock; algebra; lorentz; minkowski; direct products; multilinear; nonfiction

eBook

Published: August 1, 2015
ISBN: 9780226223063