First quantized electrodynamics

Spin-Statistics Connection for Relativistic Quantum Mechanics

“…The indefiniteness of the conserved, invariant bilinear form ψψ has impeded the development of the parametrized Dirac formalism as a relativistic extension of quantum mechanics [12,13]. In the case of The discrete symmetries for (1) are given in [14] [15]. The electromagnetic potential A µ is calculated semiclassically in [14], that is, the the source for the potential is a Møller current [6,16].…”

“…In the case of The discrete symmetries for (1) are given in [14] [15]. The electromagnetic potential A µ is calculated semiclassically in [14], that is, the the source for the potential is a Møller current [6,16]. An expansion of (1) in powers of the fine structure constant α = e 2 /4π c yields the Mott scattering cross-section at first order.…”

“…An expansion of (1) in powers of the fine structure constant α = e 2 /4π c yields the Mott scattering cross-section at first order. Combined with a partial summation that is justified for weak scattering, expansion to higher orders yields the Uehling potential, the selfenergy and self-mass of fermion lines, the anomalous magnetic moment of the electron, the Lamb shift and the axial anomaly of Quantum Electrodynamics (QED) [14]. The standard cross sections for pair interactions, such as electron-positron annihilation, may be derived from the multiple-particle parametrized Dirac equation (see Section II D) without recourse to hole theory.…”

“…± ) , and the coefficients a ± are any 2 × 1 complex matrices. Evolving the state with the free influence function Γ 0 + as constructed in [14] yields, for τ > 0,…”

“…If there is a nonvanishing external field A µ , and if Γ + (x, τ ; x ′ , τ ′ ) is the single-particle influence function constructed using Γ 0 + (x−x ′ , τ −τ ′ ) as in [6,14], then the influence function for (7) is If p × s = 0 there is in general no solution for a − such that the wavefunction ψ(x, 0)…”