理论物理的数学原理（英文版）

马天汪守宏

扉页
Chapter 1 General Introduction
+书签
1.1 Challenges of Physics and Guiding Principle
1.2 Law of Gravity, Dark Matter and Dark Energy
1.3 First Principles of Four Fundamental Interactions
1.4 Symmetry and Symmetry-Breaking
1.5 Unified Field Theory Based on PID and PRI
1.6 Theory of Strong Interactions
1.7 Theory of Weak Interactions
1.8 New Theory of Black Holes
1.9 The Universe
1.10 Supernovae Explosion and AGN Jets
1.11 Multi-Particle Systems and Unification
1.12 Weakton Model of Elementary Particles
Chapter 2 Fundamental Principles of Physics
2.1 Essence of Physics
2.1.1 General guiding principles
2.1.2 Phenomenological methods
2.1.3 Fundamental principles in physics
2.1.4 Symmetry
2.1.5 Invariance and tensors
2.1.6 Geometric interaction mechanism
2.1.7 Principle of symmetry-breaking
2.2 Lorentz Invariance
2.2.1 Lorentz transformation
2.2.2 Minkowski space and Lorentz tensors
2.2.3 Relativistic invariants
2.2.4 Relativistic mechanics
2.2.5 Lorentz invariance of electromagnetism
2.2.6 Relativistic quantum mechanics
2.2.7 Dirac spinors
2.3 Einstein s Theory of General Relativity
2.3.1 Principle of general relativity
2.3.2 Principle of equivalence
2.3.3 General tensors and covariant derivatives
2.3.4 Einstein-Hilbert action
2.3.5 Einstein gravitational field equations
2.4 Gauge Invariance
2.4.1 U (1) gauge invariance of electromagnetism
2.4.2 Generator representations of SU (N)
2.4.3 Yang-Mills action of SU (N) gauge fields
2.4.4 Principle of gauge invariance
2.5 Principle of Lagrangian Dynamics (PLD)
2.5.1 Introduction
2.5.2 Elastic waves
2.5.3 Classical electrodynamics
2.5.4 Lagrangian actions in quantum mechanics
2.5.5 Symmetries and conservation laws
2.6 Principle of Hamiltonian Dynamics (PHD)
2.6.1 Hamiltonian systems in classical mechanics
2.6.2 Dynamics of conservative systems
2.6.3 PHD for Maxwell electromagnetic fields
2.6.4 Quantum Hamiltonian systems
Chapter 3 Mathematical Foundations
3.1 Basic Concepts
3.1.1 Riemannian manifolds
3.1.2 Physical fields and vector bundles
3.1.3 Linear transformations on vector bundles
3.1.4 Connections and covariant derivatives
3.2 Analysis on Riemannian Manifolds
3.2.1 Sobolev spaces of tensor fields
3.2.2 Sobolev embedding theorem
3.2.3 Differential operators
3.2.4 Gauss formula
3.2.5 Partial differential equations on Riemannian manifolds
3.3 Orthogonal Decomposition for Tensor Fields
3.3.1 Introduction
3.3.2 Orthogonal decomposition theorems
……
Chapter 5 Elementary Particles
Chapter 6 Quantum Physics
Chapter 7 Astrophysics and Cosmology
Bibliography
Index