数学物理
作者：（美国）罗伯特·杰勒西
出版时间：2019年版
内容简介
《数学物理》是对诸如群、向量空间、拓扑空间、度量空间和希尔伯特空间等基本数学结构的导论，这些数学结构是学习相对论、粒子物理学和天体物理学等理论物理的数学基础。作者使用范畴论来强调不同数学结构之间的相互关系与数学的统一性。
目录
Chapter 1. Introduction
Chapter 2. Categories
Chapter 3. The Category of Groups
Chapter 4. Subgroups
Chapter 5. Normal Subgroups
Chapter 6. Homomorphisms
Chapter 7. Direct Products and Sums of Groups
Chapter 8. Relations
Chapter 9. The Category of Vector Spaces
Chapter 10. Subspaces
Chapter 11. Linear Mappings; Direct Products and Sums
Chapter 12. From Real to Complex Vector Spaces and Back
Chapter 13. Duals
Chapter 14. Multilinear Mappings; Tensor Products
Chapter 15. Example: Minkowski Vector Space
Chapter 16. Example: The Lorentz Group
Chapter 17. Functors
Chapter 18. The Category of Associative Algebras
Chapter 19. The Category of Lie Algebras
Chapter 20. Example: The Algebra of Observables
Chapter 21. Example: Fock Vector Space
Chapter 22. Representations: General Theory
Chapter 23. Representations on Vector Spaces
Chapter 24. The Algebraic Categories: Summary
Chapter 25. Subsets and Mappings
Chapter 26. Topological Spaces
Chapter 27. Continuous Mappings
Chapter 28. The Category of Topological Spaces
Chapter 29. Nets
Chapter 30. Compactness
Chapter 31. The Compact-Open Topology
Chapter 32. Connectedness
Chapter 33. Example: Dynamical Systems
Chapter 34. Homotopy
Chapter 35. Homology
Chapter 36. Homology: Relation to Homotopy
Chapter 37. The Homology Functors
Chapter 38. Uniform Spaces
Chapter 39. The Completion of a Uniform Space
Chapter 40. Topological Groups
Chapter 41. Topological Vector Spaces
Chapter 42. Categories: Summary
Chapter 43. Measure Spaces
Chapter 44. Constructing Measure Spaces
Chapter 45. Measurable Functions
Chapter 46. Integrals
Chapter 47. Distributions
Chapter 48. Hilbert Spaces
Chapter 49. Bounded Operators
Chapter 50. The Spectrum of a Bounded Operator
Chapter 51. The Spectral Theorem: Finite-dimensional Case
Chapter 52. Continuous Functions of a Hermitian Operator
Chapter 53. Other Functions of a Hermitian Operator
Chapter 54. The Spectral Theorem
Chapter 55. Operators (Not Necessarily Bounded)
Chapter 56. Self-Adjoint Operators
