Book
Licensed
Unlicensed
Requires Authentication
Mathematical Physics
-
Robert Geroch
Language:
English
Published/Copyright:
1984
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
-
Download PDFPublicly Available
Frontmatter
i -
Download PDFPublicly Available
Contents
v -
Requires Authentication UnlicensedLicensed
1. Introduction
1 -
Requires Authentication UnlicensedLicensed
2. Categories
3 -
Requires Authentication UnlicensedLicensed
3. The Category of Groups
16 -
Requires Authentication UnlicensedLicensed
4. Subgroups
24 -
Requires Authentication UnlicensedLicensed
5. Normal Subgroups
29 -
Requires Authentication UnlicensedLicensed
6. Homomorphisms
32 -
Requires Authentication UnlicensedLicensed
7. Direct Products and Sums of Groups
35 -
Requires Authentication UnlicensedLicensed
8. Relations
39 -
Requires Authentication UnlicensedLicensed
9. The Category of Vector Spaces
44 -
Requires Authentication UnlicensedLicensed
10. Subspaces
53 -
Requires Authentication UnlicensedLicensed
11. Linear Mappings; Direct Products and Sums
58 -
Requires Authentication UnlicensedLicensed
12. From Real to Complex Vector Spaces and Back
62 -
Requires Authentication UnlicensedLicensed
13. Duals
65 -
Requires Authentication UnlicensedLicensed
14. Multilinear Mappings; Tensor Products
71 -
Requires Authentication UnlicensedLicensed
15. Example: Minkowski Vector Space
79 -
Requires Authentication UnlicensedLicensed
16. Example: The Lorentz Group
87 -
Requires Authentication UnlicensedLicensed
17. Functors
90 -
Requires Authentication UnlicensedLicensed
18. The Category of Associative Algebras
97 -
Requires Authentication UnlicensedLicensed
19. The Category of Lie Algebras
104 -
Requires Authentication UnlicensedLicensed
20. Example: The Algebra of Observables
111 -
Requires Authentication UnlicensedLicensed
21. Example: Fock Vector Space
114 -
Requires Authentication UnlicensedLicensed
22. Representations: General Theory
120 -
Requires Authentication UnlicensedLicensed
23. Representations on Vector Spaces
125 -
Requires Authentication UnlicensedLicensed
24. The Algebraic Categories: Summary
132 -
Requires Authentication UnlicensedLicensed
25. Subsets and Mappings
134 -
Requires Authentication UnlicensedLicensed
26. Topological Spaces
136 -
Requires Authentication UnlicensedLicensed
27. Continuous Mappings
147 -
Requires Authentication UnlicensedLicensed
28. The Category of Topological Spaces
154 -
Requires Authentication UnlicensedLicensed
29. Nets
160 -
Requires Authentication UnlicensedLicensed
30. Compactness
165 -
Requires Authentication UnlicensedLicensed
31. The Compact-Open Topology
172 -
Requires Authentication UnlicensedLicensed
32. Connectedness
177 -
Requires Authentication UnlicensedLicensed
33. Example: Dynamical Systems
183 -
Requires Authentication UnlicensedLicensed
34. Homotopy
188 -
Requires Authentication UnlicensedLicensed
35. Homology
199 -
Requires Authentication UnlicensedLicensed
36. Homology: Relation to Homotopy
211 -
Requires Authentication UnlicensedLicensed
37. The Homology Functors
214 -
Requires Authentication UnlicensedLicensed
38. Uniform Spaces
217 -
Requires Authentication UnlicensedLicensed
39. The Completion of a Uniform Space
225 -
Requires Authentication UnlicensedLicensed
40. Topological Groups
234 -
Requires Authentication UnlicensedLicensed
41. Topological Vector Spaces
240 -
Requires Authentication UnlicensedLicensed
42. Categories: Summary
248 -
Requires Authentication UnlicensedLicensed
43. Measure Spaces
249 -
Requires Authentication UnlicensedLicensed
44. Constructing Measure Spaces
257 -
Requires Authentication UnlicensedLicensed
45. Measurable Functions
259 -
Requires Authentication UnlicensedLicensed
46. Integrals
262 -
Requires Authentication UnlicensedLicensed
47. Distributions
270 -
Requires Authentication UnlicensedLicensed
48. Hilbert Spaces
277 -
Requires Authentication UnlicensedLicensed
49. Bounded Operators
285 -
Requires Authentication UnlicensedLicensed
50. The Spectrum of a Bounded Operator
293 -
Requires Authentication UnlicensedLicensed
51. The Spectral Theorem: Finite-dimensional Case
302 -
Requires Authentication UnlicensedLicensed
52. Continuous Functions of a Hermitian Operator
306 -
Requires Authentication UnlicensedLicensed
53. Other Functions of a Hermitian Operator
311 -
Requires Authentication UnlicensedLicensed
54. The Spectral Theorem
319 -
Requires Authentication UnlicensedLicensed
55. Operators (Not Necessarily Bounded)
324 -
Requires Authentication UnlicensedLicensed
56. Self-Adjoint Operators
329 -
Requires Authentication UnlicensedLicensed
Index of Defined Terms
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
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;
