Mathematical Physics

Robert Geroch

Book

Mathematical Physics

Robert Geroch

Language: English

Published/Copyright: 1984

Published by

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This book is in the series

Chicago Lectures in Physics

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

Mathematics General Mathematics

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

Publishing information

Pages and Images/Illustrations in book

eBook published on:

August 1, 2015

eBook ISBN:

9780226223063

Pages and Images/Illustrations in book

Main content:

358

https://doi.org/10.7208/9780226223063

eBook ISBN: 9780226223063

Keywords for this book

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

Audience(s) for this book

Professional and scholarly;

Mathematical Physics

Overview

About this book

Author / Editor information

Topics

Table of contents

Bibliographic data