A new approach to the semi-classical relativistic two-body problem for charged fermions

Abstract

Generalizing from a recently developed hybrid formulation of classical electrodynamics with «direct (charge-field) action» structure we construct an analogous semi-classical Dirac formulation of the theory, which is capable of describing the semi-classical quantum mechanics of two identical spin-1/2 particles. This semi-classical formulation is to be used as a heuristic aid in searching for the theoretical structure of a fully «second quantized» theory. The Pauli exclusion principle is incorporated by making the interaction fields (in the action principle) antisymmetric with respect to «charge-field» labeling. In this manner, «position correlation» effects associated with «configuration interaction» can also be accounted for. By studying the nature of the stationary-state solutions, the formalism is compared with the conventional quantum-mechanical one (to understand the similarities and the differences between this approach and the usual correlated Hartree-Fock approximation of ordinary relativistic quantum theory).The stationarystate solutions to the semi-classical formalism are shown to closely approximate the usual quantum-mechanical solutions when the wave functions are represented as a superposition of Slater determinants of Dirac-Coulombic-type wave functions with radial parts having a form which extremizes the total Breit energy. The manner in which this semi-classical theory might be extended to a fully «second quantized» formalism is sketched.