Contents › Part 10

Part 10 — Relativistic Quantum Mechanics

1. The Klein–Gordon Equation
   • The equation
   • Negative energies and the indefinite density
   • Minimal coupling and the charged scalar
   • The Feshbach–Villars form and the nonrelativistic limit
   • Propagation, causality and the propagator
   • Pauli–Weisskopf: the equation is a field
   • The observed spin-0 sector
2. The Dirac Equation
   • Construction of the equation
   • Lorentz covariance and the spinor
   • Spin as a consequence, not an assumption
   • The hydrogen atom solved exactly
   • Negative energies, holes and the positron
   • Phenomena of the one-particle theory
   • The systematic nonrelativistic expansion
   • The massless limit and the boundary of the theory
3. Particles as Poincaré Representations
   • Symmetries act unitarily: Wigner's theorem
   • The unitary generators of the Poincaré group
   • The universal cover $\SL(2,\C)$
   • The invariants: mass and spin
   • Orbits, little groups, and induced representations
   • Massive particles: spin
   • Massless particles: helicity
   • The particle dictionary
4. Experiment: The Positron experiment
   • Historical context and the prediction under test
   • Apparatus
   • Procedure
   • Observations
   • Interpretation
   • Modern repetitions and precision
5. The Weyl Equation and Neutrinos
   • The two-component equation
   • The neutrino hypothesis
   • Parity and the reinstatement of the equation
   • The two-component theory of the neutrino
   • Chirality in the Standard Model
   • Mass, and where the massless picture fails
   • The Majorana question
   • Weyl fermions as an observed phenomenon
6. Higher-Spin Wave Equations
   • The classification problem
   • Spin 1: the Proca field
   • Spin 3/2: the Rarita–Schwinger field
   • Spin 2: the Fierz–Pauli field
   • General spin
   • No-go theorems
   • Experimental status
7. Experiment: Neutrino Helicity experiment
   • Historical context and the prediction under test
   • Apparatus
   • Procedure
   • Observations
   • Interpretation
   • Modern repetitions and precision