Physics
Physics is the first section to make the cross-referenced structure visible. Every claim here points back to a specific mathematical result — Lagrangians to variational calculus, field theory to representation theory, statistical mechanics to measure theory.
Units (§09–13)
09.01.01— Kinematics — position, velocity, acceleration shipped09.01.02— Newton's laws of motion draft09.01.03— Conservation laws — energy, momentum, angular momentum shipped09.02.01— The action principle and variational calculus draft09.02.02— Euler-Lagrange equations draft09.03.01— Noether's theorem — symmetries and conservation laws draft09.04.01— Legendre transform — from Lagrangian to Hamiltonian draft09.04.02— Hamilton's equations draft09.05.01— Canonical transformations draft09.05.02— Hamilton-Jacobi equation draft09.06.01— Action-angle variables draft09.07.01— Continuum Mechanics and Field Theory09.08.01— KAM theorem and chaos draft10.01.01— Coulomb's law and Gauss's law draft10.01.02— Laplace equation and boundary value problems draft10.02.01— Biot-Savart law and Ampere's law draft10.03.01— Faraday's law and electromagnetic induction draft10.04.01— Maxwell's equations in differential form draft10.04.02— EM waves and the wave equation draft10.05.01— Special relativity — postulates and Lorentz transformations draft10.05.02— Relativistic kinematics and dynamics draft10.06.01— Covariant electrodynamics — Faraday tensor draft10.07.01— Radiation from accelerating charges — Larmor formula draft11.01.01— First and second laws of thermodynamics draft11.01.02— Thermodynamic potentials and Legendre transforms draft11.02.01— Maxwell-Boltzmann distribution from kinetic theory draft11.03.01— Microcanonical ensemble draft11.04.01— Canonical ensemble and partition function draft11.05.01— Bose-Einstein distribution draft11.05.02— Fermi-Dirac distribution and electron gas draft11.06.01— Ising model and phase transitions draft11.07.01— Critical phenomena and renormalization group draft12.01.01— Wave-particle duality and the double-slit shipped12.01.02— Stern-Gerlach and spin-1/2 draft12.02.01— Hilbert-space formalism of quantum mechanics draft12.02.02— Operators, observables, and Hermiticity draft12.03.01— Schrödinger and Heisenberg pictures draft12.04.01— Particle in a box shipped12.04.02— Quantum harmonic oscillator draft12.05.01— Angular momentum operators and SU(2) representations draft12.06.01— Hydrogen atom bound states draft12.07.01— Time-independent perturbation theory draft12.07.02— Time-dependent perturbation theory and Fermi's golden rule shipped12.08.01— Scattering Theory12.09.01— Identical Particles and Many-Body Quantum Mechanics12.10.01— Path integral formulation of quantum mechanics draft12.11.01— Dirac equation and relativistic spin draft12.12.01— Canonical Quantum Field Theory12.13.01— Bosonic Fock space and second quantisation shipped12.13.02— Fermionic Fock space, Pauli exclusion, and anticommutators shipped13.01.01— The equivalence principle draft13.02.01— Tensors on smooth manifolds shipped13.02.02— Geodesics and parallel transport shipped13.03.01— Riemann curvature tensor draft13.04.01— Einstein field equations draft13.05.01— Schwarzschild solution draft13.05.02— Orbits in Schwarzschild geometry draft13.06.01— Black Holes13.07.01— Linearized GR and gravitational waves draft13.08.01— FLRW cosmology and Friedmann equations shipped
Five-branch structure
§09 classical mechanics · §10 electromagnetism & special relativity · §11 statistical mechanics (physics flavor) · §12 quantum mechanics & QFT · §13 general relativity & cosmology. Plus existing §03 math-physics border units (Clifford, spin, Dirac, Yang-Mills, Atiyah-Singer) and §08 math-stat-mech (Onsager, RG, lattice gauge). See the physics plan for branch-by-branch detail.