On the theory of interacting fields in Foldy-Wouthuysen representation

TL;DR

This paper develops a quantum electrodynamics framework in the Foldy-Wouthuysen representation, calculating key processes and exploring particle-antiparticle interactions, invariance properties, and symmetry breaking effects.

Contribution

It introduces a nonlocal Hamiltonian approach in the FW representation, specifies Feynman rules, and demonstrates a novel method for including real particle-antiparticle interactions with negative mass particles.

Findings

Calculated QED processes like Coulomb scattering, Compton effect, Lamb shift.

Showed invariance of QED in FW representation under C, P, T transformations.

Proposed a method to incorporate real particle-antiparticle interactions via negative mass particles.

Abstract

The paper considers quantum electrodynamics (QED) and weak interaction of elementary particles in the lower orders of the perturbation theory using nonlocal Hamiltonian in the Foldy-Wouthuysen (FW) representation. Feynman rules in the FW representation are specified, specific QED processes are calculated. Cross sections of Coulomb scattering of electrons, Muller scattering, Compton effect, electron self-energy, vacuum polarization, anomalous magnetic moment of electron, Lamb shift of atomic energy levels are calculated. The possibility of the scattering matrix expansion in powers of the coupling constant, in which matrix elements contain no terms with fermion propagators, is demonstrated for external fermion lines corresponding to real particles (antiparticles). It is shown that a method to include the interaction of real particles with antiparticles in the FW representation is to introduce negative mass particles and antiparticles to the theory. The theory is degenerate with respect to the particle (antiparticle) mass sign, however the masses of the particle and antiparticle interacting with each other should be of opposite sign. QED in the FW representation is invariant under C, P, T inversions. The weak interaction breaks the C and P invariance, but preserves the combined CP parity. In the theory there is a possibility to relate the break of CP invariance to total or partial removal of the degeneracy in particle (antiparticle) mass sign.