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    • 数学物理(英文版)
      • 作者:(美)罗伯特·杰勒西
      • 出版社:世界图书出版公司
      • ISBN:9787519266448
      • 出版日期:2019/09/01
      • 页数:351
    • 售价:23.6
  • 内容大纲

        本书是对诸如群、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。
  • 作者介绍

  • 目录

    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 Space
    22.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: Summary
    43.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

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