物理学中的拓扑与几何（英文影印版）
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
查看完整
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
查看完整
《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》讲述了在物理学中应用的拓扑和几何知识，包括流形、张量场、流形上的微积分、纤维丛理论等。特别地，《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》讲解了这些理论在物理学中的诸多应用。
随着理论物理的发展，拓扑与几何这些数学理论在物理中的应用日益广泛。特别地，在理论物理近些年的一些新理论中，拓扑和几何的应用更加重要。《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》系统而深入，其引进能够给理论物理工作者以很大帮助。
随着理论物理的发展，拓扑与几何这些数学理论在物理中的应用日益广泛。特别地，在理论物理近些年的一些新理论中，拓扑和几何的应用更加重要。《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》系统而深入，其引进能够给理论物理工作者以很大帮助。
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
3.7.1 Classical Point Mechanics
3.7.2 Classical and Quantum Mechanics
3.7.3 Classical Point Mechanics Under Momentum Constraints
3.7.4 Classical Mechanics Under Velocity Constraints
3.7.5 Thermodynamics
References
4 Tensor Fields
4.1 Tensor Algebras
4.2 Exterior Algebras
4.3 Tensor Fields and Exterior Forms
4.4 Exterior Differential Calculus
References
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
References
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
References
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
References
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
8.6.1 Berry-Simon Connection
8.6.2 Degenerate Case
8.6.3 Electrical Polarization
8.6.4 Orbital Magnetism
8.6.5 Topological Insulators
8.7 Gauge Field Theory of Molecular Physics
References
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~ihlerian Manifolds
References
Compendium
List of Symbols
Index
^ 收 起
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
3.7.1 Classical Point Mechanics
3.7.2 Classical and Quantum Mechanics
3.7.3 Classical Point Mechanics Under Momentum Constraints
3.7.4 Classical Mechanics Under Velocity Constraints
3.7.5 Thermodynamics
References
4 Tensor Fields
4.1 Tensor Algebras
4.2 Exterior Algebras
4.3 Tensor Fields and Exterior Forms
4.4 Exterior Differential Calculus
References
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
References
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
References
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
References
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
8.6.1 Berry-Simon Connection
8.6.2 Degenerate Case
8.6.3 Electrical Polarization
8.6.4 Orbital Magnetism
8.6.5 Topological Insulators
8.7 Gauge Field Theory of Molecular Physics
References
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~ihlerian Manifolds
References
Compendium
List of Symbols
Index
^ 收 起
《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》讲述了在物理学中应用的拓扑和几何知识，包括流形、张量场、流形上的微积分、纤维丛理论等。特别地，《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》讲解了这些理论在物理学中的诸多应用。
随着理论物理的发展，拓扑与几何这些数学理论在物理中的应用日益广泛。特别地，在理论物理近些年的一些新理论中，拓扑和几何的应用更加重要。《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》系统而深入，其引进能够给理论物理工作者以很大帮助。
随着理论物理的发展，拓扑与几何这些数学理论在物理中的应用日益广泛。特别地，在理论物理近些年的一些新理论中，拓扑和几何的应用更加重要。《中外物理学精品书系：物理学中的拓扑与几何（英文 影印版）》系统而深入，其引进能够给理论物理工作者以很大帮助。
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