Nonperturbative theory of Coulombic retardation in relativistic quantum mechanics

Abstract

Retardation causes the Coulomb field of a moving point particle to be pinched in a direction transverse to the direction of the particle's velocity. The pinch is expected to be strong as the velocity approaches the speed of light, a situation which arises at small interparticle distances between particles of opposite charge and equal mass, where the motion would be expected to be strongly one-dimensional and hence strongly binding in the direction of the pinch. The Klein–Gordon and Dirac equations are solved for this situation; the results suggest that an alternative interpretation for positron–electron annihilation might be two-photon decay to a quantum state describing strong two-body binding in the direction of the pinch of the retarded potential. The alternative interpretation is supported by the fundamental relativistic energy–momentum relation, ( E− V) 2= m 2 c 4+ c 2 p 2, which guarantees, for a removable V 2 singularity at the origin, that the energy goes to zero as the quantum-mechanical mean of V goes to −∞. In the present strong-binding theory any residual mass between zero mass (Dirac interpretation) and the mass implied by the imprecision of energy-release measurements is consistent with existing experimental knowledge of annihilation.