Contents
An evidence-based account of theoretical, mathematical, and experimental physics. SI units, axiomatically. Every observed phenomenon with its derivation.
complete
pending derivations inside
stub / reserved heading
-
Part 2 — Mathematical Methods
-
Ordinary Differential Equations and Sturm–Liouville Theory
-
The semiclassical approximation
- The equation and its Sturm–Liouville data
- The expansion in powers of $\hbar$
- Where the approximation is valid, and where it is not
- Connection across a simple turning point
- Turning points of higher order
- Barrier penetration and the Gamow factor
- Bohr–Sommerfeld quantisation and the Maslov index
- Worked example: a charged particle against a Coulomb barrier
- The radial equation
- The Langer substitution
- Boundary layers and matched asymptotic expansions
- The Laplace transform
- Summary of the classical families
-
Differentiable Manifolds, Tensors, and Curvature
- Index conventions and the symmetry ladder
-
Differentiable manifolds
-
Charts, atlases, and differentiable structure
- Coordinate systems
- Coordinates
- Atlases
- Differentiable maps on a topological space
- Differentiable structure
- Differentiable manifold
- Diffeomorphism
- The differential of a smooth map
- Immersion, embedding, and submanifold
- Product of manifolds
- Hypersurfaces
- Higher codimension and maps of constant rank
- Group actions and quotient manifolds
-
-
Tensor analysis on manifolds
-
Tensors under general coordinate transformations
- General coordinate transformations
- Transformation law of a vector
- Contravariant, covariant, and mixed tensors
- The displacement vector
- Scalars and invariance
- Scalar product
- The Kronecker delta as a mixed tensor
- Symmetry and antisymmetry
- Symmetric and antisymmetric parts
- The vector-product tensor
- Gradient of a scalar
- A Jacobian identity
- Vielbein and local frames
- Curvature
- The Cartan formalism
-
Expansions of Lie Algebras
- The tensor product construction
- Ideals, the radical, and the Killing form
- The Takiff tower
- Central charges as the top level of an expansion
- Invariant forms and why the extension is needed
- Relation to the published expansion methods
- The construction in $3{+}1$ dimensions
- Positive functionals and the Gram form
-
Part 3 — Classical Mechanics
-
Experiment: Free Fall and Projectile Motion experiment
-
Experiment: The Cavendish Torsion Balance experiment
-
Experiment: The Pendulum experiment
-
Experiment: Waves and Acoustics experiment
-
Experiment: Fluid Flow and Turbulence experiment
-
Part 5 — General Relativity and Cosmology
-
Experiment: Gravitational Waves experiment
-
Experiment: Black-Hole Observations experiment
-
Experiment: The Cosmic Microwave Background experiment
-
Part 6 — Classical Thermodynamics 7 pending
-
Classical Thermodynamics 1 pending
-
Kinetic Theory of Gases 2 pending
-
Experiment: The Mechanical Equivalent of Heat experiment 1 pending
-
Experiment: The Kinetic Theory Tested experiment 3 pending
-
-
Part 7 — Classical Field Theory and Electrodynamics 35 pending
-
Electrostatics 4 pending
-
Magnetostatics 3 pending
-
The Maxwell Equations 3 pending
-
Electromagnetic Waves and Optics 4 pending
-
Electrodynamics in Matter 5 pending
-
Experiments: Electromagnetism experiment 3 pending
-
Generalized Classical Field Theory 1 pending
-
Plasmas and Magnetohydrodynamics 5 pending
-
Experiment: Wave Optics experiment 4 pending
-
-
Part 8 — The Transition to Quantum Physics 35 pending
-
Atomic Models and Spectra 6 pending
-
Matter Waves 7 pending
-
Experiment: Franck–Hertz experiment 3 pending
-
Experiment: The Blackbody Spectrum Measured experiment 1 pending
-
Experiment: The Photoelectric Effect and Compton Scattering experiment 3 pending
-
Experiment: Matter Waves Observed experiment 2 pending
-
Experiment: X-ray Spectra and the Charge of the Nucleus experiment 3 pending
-
Part 9 — Quantum Mechanics 34 pending
-
The Postulates of Quantum Mechanics 3 pending
-
Elementary Quantum Systems 3 pending
-
Angular Momentum and Spin 2 pending
-
The Hydrogen Atom 5 pending
-
Approximation Methods 1 pending
-
Identical Particles 4 pending
-
Entanglement and Bell Tests 1 pending
-
Interpretations (Evidence-Anchored) 1 pending
-
Scattering Theory 1 pending
-
Open Quantum Systems and Decoherence 2 pending
-
Atoms and Molecules 2 pending
-
Experiment: Bell Tests experiment 2 pending
-
Experiment: Precision Spectroscopy and Atomic Clocks experiment 1 pending
-
Experiment: Quantum Tunnelling Observed experiment 3 pending
-
-
Part 10 — Relativistic Quantum Mechanics 19 pending
-
The Klein–Gordon Equation 2 pending
-
The Dirac Equation 3 pending
-
Particles as Poincaré Representations 2 pending
-
Experiment: The Positron experiment 3 pending
-
The Weyl Equation and Neutrinos 4 pending
-
Higher-Spin Wave Equations 1 pending
-
Experiment: Neutrino Helicity experiment 4 pending
-
-
Part 11 — Quantum Field Theory and the Standard Model 82 pending
-
Canonical Quantization of Fields 4 pending
-
Quantum Electrodynamics and Renormalization 10 pending
-
Weak Interactions 3 pending
-
Quantum Chromodynamics 4 pending
-
Flavour Physics and Neutrinos 5 pending
-
Discrete Symmetries and CPT 3 pending
-
Path-Integral Quantization 5 pending
-
Nuclear Forces and Nuclear Structure 8 pending
-
The Renormalization Group 6 pending
-
Axiomatic Quantum Field Theory 8 pending
-
Experiment: Parity Violation experiment 4 pending
-
Experiment: CP Violation experiment 3 pending
-
Experiment: The Electron Anomalous Magnetic Moment experiment 2 pending
-
Experiment: The Higgs Boson Discovery experiment 4 pending
-
Experiment: Neutrino Oscillations experiment
-
Cosmic Rays and Astroparticle Physics 5 pending
-
Experiment: Deep Inelastic Scattering experiment 4 pending
-
Experiment: Artificial Transmutation and the Instruments of Nuclear Physics experiment 1 pending
-
-
Part 12 — Statistical Mechanics 62 pending
-
Statistical Mechanics 1 pending
-
Experiment: Brownian Motion and Avogadro's Number experiment 4 pending
-
Quantum Statistics 5 pending
-
Experiment: Bose–Einstein Condensation experiment 4 pending
-
Quantum Optics and the Photon 3 pending
-
Phase Transitions and Critical Phenomena 5 pending
-
Phonons and Lattice Dynamics 4 pending
-
Electrons in Solids: Band Theory 6 pending
-
Semiconductors 5 pending
-
Experiment: The Quantum Hall Effect experiment 6 pending
-
Magnetism in Matter 3 pending
-
Superconductivity and Superfluidity 6 pending
-
Experiment: Superconductivity experiment 5 pending
-
Experiment: Neutron Scattering and the Structure of Solids experiment 4 pending
-
-
Part 13 — Frontiers and Open Problems 6 pending
Appendices