Physics

Notes on the formal structure of modern physics, organized around the postulational presentations of quantum mechanics and quantum field theory.

Contents

1. Special Relativity — the kinematic and dynamical framework of flat spacetime: postulates, the invariant interval, the Lorentz/Poincaré group, four-vectors, and covariant electromagnetism.
2. General Relativity — the geometrization of gravity: the equivalence principle, spacetime as a curved Lorentzian manifold, the covariant derivative and curvature, and the Einstein field equations.
3. Quantum Mechanics — non-relativistic QM presented from its seven standard postulates, plus the Heisenberg and path-integral reformulations.
4. Quantum Field Theory — relativistic QFT in the Wightman axiomatic style: postulates, the modern Wigner–Weinberg derivation, Fock space, observables (cross sections, decay rates, collider measurements), and specific theories (QED, QCD, electroweak, the Standard Model).

Mathematical prerequisites

The physics pages assume working familiarity with the structures collected in the Mathematics section:

• Group theory — abstract and finite groups, Lie groups, Lie algebras, representations.
• Clifford algebras — for Dirac spinors and relativistic fermions.
• Topology and manifolds — for spacetime and gauge-bundle backgrounds.
• Geometry — metric geometry and curvature, for the general-relativity pages.

Reading order

SR → GR for the relativistic/gravitational track, and QM → QFT for the quantum track. General relativity builds on the four-vector and Lorentz-group machinery of special relativity; within GR the equivalence principle → geometry → covariant derivative → curvature → field equations chain is linear. Within QFT the preliminaries → postulates → modern foundations → Fock space → particles-as-excitations chain is linear; the observables and specific theories subtrees are independent and can be read in any order.