- 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
- 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 viii CONTENTS
- 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 ofSU(N)
- 2.4.3 Yang-Mills action ofSU(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.
- 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 ofSU(N).
- 3.5.3 SU(N)tensors CONTENTS ix
- 3.5.4 Intrinsic Riemannian metric onSU(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
- 4 Unified Field Theory
- 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. x CONTENTS
- 4.6.5 Introduction to the classical electroweak theory.
- 4.6.6 Problems in WS theory.
- 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 ofSU(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 w∗-color algebra
- 5.5.5 Mediator clouds of subatomic particles
- 6 Quantum Physics
- 6.1 Introduction.
- 6.2 Foundations of Quantum Physics.
- 6.2.1 Basic postulates.
- 6.2.2 Quantum dynamic equations.
- 6.2.3 Heisenberg uncertainty relation and Pauli exclusionprinciple.
- 6.2.4 Angular momentum rule
- 6.3 Solar Neutrino Problem. CONTENTS xi
- 6.3.1 Discrepancy of the solar neutrinos.
- 6.3.2 Neutrino oscillations
- 6.3.3 Mixing matrix and neutrino masses
- 6.3.4 MSW effect.
- 6.3.5 Massless neutrino oscillation model
- 6.3.6 Neutrino non-oscillation mechanism.
- 6.4 Energy Levels of Subatomic Particles
- 6.4.1 Preliminaries
- 6.4.2 Spectral equations of bound states.
- 6.4.3 Charged leptons and quarks
- 6.4.4 Baryons and mesons
- 6.4.5 Energy spectrum of mediators
- 6.4.6 Discreteness of energy spectrum.
- 6.5 Field Theory of Multi-Particle Systems
- 6.5.1 Introduction.
- 6.5.2 Basic postulates forN-body quantum physics.
- 6.5.3 Field equations of multi-particle systems
- 6.5.4 Unified field model coupling matter fields.
- 6.5.5 Atomic spectrum.
- 7 Astrophysics and Cosmology
- 7.1 Astrophysical Fluid Dynamics
- 7.1.1 Fluid dynamic equations on Riemannian manifolds.
- 7.1.2 Schwarzschild and Tolman-Oppenheimer-Volkoff (TOV) metrics.
- 7.1.3 Differential operators in spherical coordinates.
- 7.1.4 Momentum representation
- 7.1.5 Astrophysical Fluid Dynamics Equations
- 7.2 Stars.
- 7.2.1 Basic knowledge
- 7.2.2 Main driving force for stellar dynamics
- 7.2.3 Stellar interior circulation
- 7.2.4 Stellar atmospheric circulations
- 7.2.5 Dynamics of stars with variable radii
- 7.2.6 Mechanism of supernova explosion
- 7.3 Black Holes.
- 7.3.1 Geometric realization of black holes.
- 7.3.2 Blackhole theorem
- 7.3.3 Criticalδ-factor
- 7.3.4 Origin of stars and galaxies.
- 7.4 Galaxies.
- 7.4.1 Introduction.
- 7.4.2 Galaxy dynamics.
- 7.4.3 Spiral galaxies
- 7.4.4 Active galactic nuclei (AGN) and jets
- 7.5 The Universe
- 7.5.1 Classical theory of the Universe xii CONTENTS
- 7.5.2 Globular universe with boundary.
- 7.5.3 Spherical Universe without boundary
- 7.5.4 New cosmology
- 7.6 Theory of Dark Matter and Dark energy
- 7.6.1 Dark energy and dark matter phenomena
- 7.6.2 PID cosmological model and dark energy.
- 7.6.3 PID gravitational interaction formula
- 7.6.4 Asymptotic repulsion of gravity
- 7.6.5 Simplified gravitational formula
- 7.6.6 Nature of dark matter and dark energy.
- Index
rick simeone
(Rick Simeone)
#1