Chapter 1 General Introduction 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 3.3.3 Uniqueness of orthogonal decompositions 3.3.4 Orthogonal decomposition on manifolds with boundary 3.4 Variations with divA—Free Constraints 3.4.1 Classical variational principle 3.4.2 Derivative operators of the Yang—Mills functionals 3.4.3 Derivative operator of the Einstein—Hilbert functional 3.4.4 Variational principle with divA—free constraint 3.4.5 Scalar potential theorem 3.5 SU （N） Representation Invariance 3.5.1 SU （N） gauge representation 3.5.2 Manifold structure of SU （N） 3.5.3 SU（N） tensors 3.5.4 Intrinsic Riemannian metric on SU（N） 3.5.5 Representation invariance of gauge theory 3.6 Spectral Theory of Differential Operators 3.6.1 Physical background 3.6.2 Classical spectral theory 3.6.3 Negative eigenvalues of elliptic operators 3.6.4 Estimates for number of negative eigenvalues 3.6.5 Spectrum of Weyl operators Chapter 4 Unified Field Theory of Four Fundamental Interactions 4.1 Principles of Unified Field Theory 4.1.1 Four interactions and their interaction mechanism 4.1.2 General introduction to unified field theory 4.1.3 Geometry of unified fields 4.1.4 Gauge symmetry—breaking 4.1.5 PID and PRI 4.2 Physical Supports to PID 4.2.1 Dark matter and dark energy 4.2.2 Non well—posedness of Einstein field equations 4.2.3 Higgs mechanism and mass generation 4.2.4 Ginzburg—Landau superconductivity 4.3 Unified Field Model Based on PID and PRI 4.3.1 Unified field equations based on PID 4.3.2 Coupling parameters and physical dimensions 4.3.3 Standard form of unified field equations 4.3.4 Potentials of the weak and strong forces 4.3.5 Gauge—fixing problem 4.4 Duality and Decoupling of Interaction Fields 4.4.1 Duality 4.4.2 Gravitational field equations derived by PID 4.4.3 Modified QED model 4.4.4 Strong interaction field equations 4.4.5 Weak interaction field equations 4.5 Strong Interaction Potentials 4.5.1 Strong interaction potential of elementary particles 4.5.2 Layered formulas of strong interaction potentials 4.5.3 Quark confinement 4.5.4 Asymptotic freedom 4.5.5 Modified Yukawa potential 4.5.6 Physical conclusions for nucleon force 4.5.7 Short—range nature of strong interaction 4.6 Weak Interaction Theory 4.6.1 Dual equations of weak interaction potentials 4.6.2 Layered formulas of weak forces 4.6.3 Physical conclusions for weak forces 4.6.4 PID mechanism of spontaneous symmetry breaking 4.6.5 Introduction to the classical electroweak theory 4.6.6 Problems in WS theory Chapter 5 Elementary Particles 5.1 Basic Knowledge of Particle Physics 5.1.1 Classification of particles 5.1.2 Quantum numbers 5.1.3 Particle transitions 5.1.4 Conservation laws 5.1.5 Basic data of particles 5.2 Quark Model 5.2.1 Eightfold way 5.2.2 Irreducible representations of SU（N） 5.2.3 Physical explanation of irreducible representations 5.2.4 Computations for irreducible representations 5.2.5 Sakata model of hadrons 5.2.6 Gell—Mann—Zweig's quark model 5.3 Weakton Model of Elementary Particles 5.3.1 Decay means the interior structure 5.3.2 Theoretical foundations for the weakton model 5.3.3 Weaktons and their quantum numbers 5.3.4 Weakton constituents and duality of mediators 5.3.5 Weakton confinement and mass generation 5.3.6 Quantum rules for weaktons 5.4 Mechanisms of Subatomic Decays and Electron Radiations 5.4.1 Weakton exchanges 5.4.2 Conservation laws 5.4.3 Decay types 5.4.4 Decays and scatterings 5.4.5 Electron structure 5.4.6 Mechanism of bremsstrahlung 5.5 Structure of Mediator Clouds Around Subatomic Particles 5.5.1 Color quantum number 5.5.2 Gluons 5.5.3 Color algebra 5.5.4 ω—color algebra 5.5.5 Mediator clouds of subatomic particles …… Chapter 6 Quantum Physics Chapter 7 Astrophysics and Cosmology Bibliography Index
