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數(shù)學(xué)物理

數(shù)學(xué)物理

定 價(jià):¥59.00

作 者: 羅伯特·杰勒西
出版社: 世界圖書出版公司
叢編項(xiàng):
標(biāo) 簽: 暫缺

ISBN: 9787519266448 出版時(shí)間: 2019-09-01 包裝:
開本: 頁(yè)數(shù): 字?jǐn)?shù):  

內(nèi)容簡(jiǎn)介

  《數(shù)學(xué)物理》是對(duì)諸如群、向量空間、拓?fù)淇臻g、度量空間和希爾伯特空間等基本數(shù)學(xué)結(jié)構(gòu)的導(dǎo)論,這些數(shù)學(xué)結(jié)構(gòu)是學(xué)習(xí)相對(duì)論、粒子物理學(xué)和天體物理學(xué)等理論物理的數(shù)學(xué)基礎(chǔ)。作者使用范疇論來(lái)強(qiáng)調(diào)不同數(shù)學(xué)結(jié)構(gòu)之間的相互關(guān)系與數(shù)學(xué)的統(tǒng)一性。 \n

作者簡(jiǎn)介

  羅伯特·杰勒西(Robert Geroch)是美國(guó)著名理論物理學(xué)家,芝加哥大學(xué)教授。他的研究領(lǐng)域主要是廣義相對(duì)論和數(shù)學(xué)物理,他推廣了范疇論在數(shù)學(xué)和物理中的應(yīng)用。

圖書目錄

Chapter 1. Introduction

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Chapter 2. Categories

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Chapter 3. The Category of Groups

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Chapter 4. Subgroups

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Chapter 5. Normal Subgroups

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Chapter 6. Homomorphisms

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Chapter 7. Direct Products and Sums of Groups

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Chapter 8. Relations

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Chapter 9. The Category of Vector Spaces

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Chapter 10. Subspaces

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Chapter 11. Linear Mappings; Direct Products and Sums

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Chapter 12. From Real to Complex Vector Spaces and Back

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Chapter 13. Duals

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Chapter 14. Multilinear Mappings; Tensor Products

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Chapter 15. Example: Minkowski Vector Space

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Chapter 16. Example: The Lorentz Group

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Chapter 17. Functors

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Chapter 18. The Category of Associative Algebras

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Chapter 19. The Category of Lie Algebras

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Chapter 20. Example: The Algebra of Observables

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Chapter 21. Example: Fock Vector Space

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Chapter 22. Representations: General Theory

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Chapter 23. Representations on Vector Spaces

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Chapter 24. The Algebraic Categories: Summary

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Chapter 25. Subsets and Mappings

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Chapter 26. Topological Spaces

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Chapter 27. Continuous Mappings

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Chapter 28. The Category of Topological Spaces

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Chapter 29. Nets

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Chapter 30. Compactness

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Chapter 31. The Compact-Open Topology

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Chapter 32. Connectedness

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Chapter 33. Example: Dynamical Systems

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Chapter 34. Homotopy

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Chapter 35. Homology

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Chapter 36. Homology: Relation to Homotopy

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Chapter 37. The Homology Functors

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Chapter 38. Uniform Spaces

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Chapter 39. The Completion of a Uniform Space

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Chapter 40. Topological Groups

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Chapter 41. Topological Vector Spaces

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Chapter 42. Categories: Summary

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Chapter 43. Measure Spaces

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Chapter 44. Constructing Measure Spaces

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Chapter 45. Measurable Functions

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Chapter 46. Integrals

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Chapter 47. Distributions

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Chapter 48. Hilbert Spaces

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Chapter 49. Bounded Operators

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Chapter 50. The Spectrum of a Bounded Operator

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Chapter 51. The Spectral Theorem: Finite-dimensional Case

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Chapter 52. Continuous Functions of a Hermitian Operator

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Chapter 53. Other Functions of a Hermitian Operator

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Chapter 54. The Spectral Theorem

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Chapter 55. Operators (Not Necessarily Bounded)

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Chapter 56. Self-Adjoint Operators

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