The Dirac Equation

angular momentum antiunitary assume asymptotic completeness calculation commutes compact corresponding Coulomb covariant covering group defined denote dense described differential Dirac equation Dirac operator domain eigenfunctions eigenvalues electron essential spectrum essentially self-adjoint evolution external field finite Fock space Fredholm free Dirac operator function given Hence Hilbert space implies inducing representation invariant irreducible Ker Q Lemma Lorentz magnetic field Math mc² mKdV equation multiplication negative energy nonrelativistic limit Notes obtain operator H particle pcont Phys Poincaré group Poincaré transformation problem projective representation Proof quantum mechanics relativistic Remark satisfies scalar potential scattering operator scattering theory Schrödinger operator Sect self-adjoint operator sgn Q soliton solution spectral square integrable subgroup subspaces summand supercharge supersymmetric symmetric Theorem trace class Ueven unitarily unitary operator unitary representation vanishes vector potential wavefunction