Nonperturbative theory of Coulombic retardation in relativistic quantum mechanics

Retardation causes the Coulomb field of a moving point particle to be pinch ed in a direction transverse to the direction of the particle's velocity. T he pinch is expected to be strong as the velocity approaches the speed of l ight, a situation which arises at small interparticle distances between par ticles of opposite charge and equal mass, where the motion would be expecte d to be strongly one-dimensional and hence strongly binding in the directio n of the pinch. The Klein-Gordon and Dirac equations are solved for this si tuation; the results suggest that an alternative interpretation for positro n-electron annihilation might be two-photon decay to a quantum state descri bing strong two-body binding in the direction of the pinch of the retarded potential. The alternative interpretation is supported by the fundamental r elativistic energy-momentum relation, (E - V)(2) = m(2)c(4) + c(2)p(2), whi ch guarantees, for a removable V-2 singularity at the origin, that the ener gy goes to zero as the quantum-mechanical mean of V goes to -infinity. In t he 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 annihila tion. (C) 2000 Elsevier Science B.V. All rights reserved.