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Mathematical physics /
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 mos...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chicago :
University of Chicago Press,
1985.
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| Colección: | Chicago lectures in physics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1 . Introduction; 2 . Categories; 3. The Category of Groups; 4. Subgroups; 5 . Normal Subgroups; 6. Homomorphisms; 7. Direct Products and Sums of Groups; 8. Relations; 9. The Category of Vector Spaces; 10 . Subspaces; 11 . Linear Mappings; Direct Products and Sums; 12 . From Real to Complex Vector Spaces and Back; 13 . Duals; 14 . Multilinear Mappings; Tensor Products; 15 . Example: Minkowski Vector Space; 16 . Example: The Lorentz Group; 17 . Functors; 18 . The Category of Associative Algebras; 19 . The Category of Lie Algebras; 20 . Example: The Algebra of Observables.
- 21. Example: Fock Vector Space22. Representations: General Theory; 23 . Representations on Vector Spaces; 24 . The Algebraic Categories: Summary; 25 . Subsets and Mappings; 26. Topological Spaces; 27. Continuous Mappings; 28 . The Category of Topological Spaces; 29. Nets; 30. Compactness; 31. The Compact-Open Topology; 32. Connectedness; 33. Example: Dynamical Systems; 34. Homotopy; 35. Homology; 36. Homology: Relation to Homotopy; 37. The Homology Functors; 38. Uniform Spaces; 39. The Completion of a Uniform Space; 40. Topological Groups; 41. Topological Vector Spaces.
- 42. Categories: Summary43. Measure Spaces; 44. Constructing Measure Spaces; 45. Measurable Functions; 46. Integrals; 47. Distributions; 48. Hilbert Spaces; 49. Bounded Operators; 50. The Spectrum of a Bounded Operator; 51. The Spectral Theorem: Finite-dimensional Case; 52. Continuous Functions of a Hermitian Operator; 53. Other Functions of a Hermitian Operator; 54. The Spectral Theorem; 55. Operators (Not Necessarily Bounded); 56. Self-Adjoint Operators; Index of Defined Terms.