《物理學中的拓撲與幾何（英文影印版）》是2014年北京大學出版社出版的圖書，作者是埃施里格。
基本介紹
- 中文名：物理學中的拓撲與幾何（英文影印版）
- 書號：24830
- 作者：(德)埃施里格(H. Eschrig)
- 開本：大32開
- 字數：486 千字
- 瀏覽次數：462
- 出版日期：2014年10月22日
- ISBN：9787301248300
- 版次：1
- 裝訂：平
- 定價：69 元
- 叢書名：中外物理學精品書系
內容簡介,章節目錄,
內容簡介
本書講述了在物理學中套用的拓撲和幾何知識，包括流形、張量場、流形上的微積分、纖維叢理論等。特別地，本書講解了這些理論在物理學中的諸多套用。 隨著理論物理的發展，拓撲與幾何這些數學理論在物理中的套用日益廣泛。特別地，在理論物理近些年的一些新理論中，拓撲和幾何的套用更加重要。本書系統而深入，其引進能夠給理論物理工作者以很大幫助
章節目錄
1 Introduction
References
2 Topology
2.1 Basic Definitions
2.2 Base of Topology, Metric, Norm.
2.3 Derivatives
2.4 Compactness
2.5 Connectedness, Homotopy
2.6 Topological Charges in Physics.
References
3 Manifolds
3.1 Charts and Atlases
3.2 Smooth Manifolds
3.3 Tangent Spaces
3.4 Vector Fields
3.5 Mappings of Manifolds, Submanifolds
3.6 Frobenius' Theorem.
3.7 Examples from Physics .
4 Tensor Fields. .
4.1 Tensor Algebras
4.2 Exterior Algebras
4.3 Tensor Fields and Exterior Forms
4.4 Exterior Differential Calculus
5 Integration, Homology and Cohomology
5.1 Prelude in Euclidean Space.
5.2 Chains of Simplices .
5.3 Integration of Differential Forms
5.4 De Rham Cohomology.
5.5 Homology and Homotopy.
5.6 Homology and Cohomology of Complexes.
5.7 Euler's Characteristic
5.8 Critical Points .
5.9 Examples from Physics
6 Lie Groups
6.1 Lie Groups and Lie Algebras
6.2 Lie Group Homomorphisms and Representations
6.3 Lie Subgroups.
6.4 Simply Connected Covering Group
6.5 The Exponential Mapping.
6.6 The General Linear Group Gl(n,K) .
6.7 Example from Physics: The Lorentz Group
6.8 The Adjoint Representation
7 Bundles and Connections
7.1 Principal Fiber Bundles
7.2 Frame Bundles
7.3 Connections on Principle Fiber Bundles
7.4 Parallel Transport and Holonomy
7.5 Exterior Covariant Derivative and Curvature Form
7.6 Fiber Bundles .
7.7 Linear and Affine Connections
7.8 Curvature and Torsion Tensors .
7.9 Expressions in Local Coordinates on M
8 Parallelism, Holonomy, Homotopy and (Co)homology .
8.1 The Exact Homotopy Sequence.
8.2 Homotopy of Sections
8.3 Gauge Fields and Connections on R4.
8.4 Gauge Fields and Connections on Manifolds
8.5 Characteristic Classes.
8.6 Geometric Phases in Quantum Physics.
8.7 Gauge Field Theory of Molecular Physics
9 Riemannian Geometry .
9.1 Riemannian Metric
9.2 Homogeneous Manifolds
9.3 Riemannian Connection .
9.4 Geodesic Normal Coordinates
9.5 Sectional Curvature .
9.6 Gravitation . .
9.7 Complex, Hermitian and K?hlerian Manifolds.
List of Symbols
Index .
