Light-Cone Expansion of the Dirac Sea with Light Cone Integrals

TL;DR

This paper develops a method to analyze the Dirac sea near the light cone using integrals over distributions, providing asymptotic formulas that simplify calculations in quantum field theory.

Contribution

It introduces a light-cone expansion technique for the Dirac sea using light cone integrals, connecting position and momentum space methods.

Findings

Derived asymptotic formulas for light cone integrals

Provided line integral representations involving the external potential

Simplified calculations of the Dirac sea near the light cone

Abstract

The Dirac sea is calculated in an expansion around the light cone. The method is to analyze the perturbation expansion for the Dirac sea in position space. This leads to integrals over expressions containing distributions which are singular on the light cone. We derive asymptotic formulas for these "light cone integrals" in terms of line integrals over the external potential and its partial derivatives. The calculations are based on the perturbation expansion for the Dirac sea in the preprint gr-qc/9606040 and yield the formulas listed in the appendix of this preprint. The results can be obtained easier with a combination of calculations in position and momentum space (see the corresponding preprints on the hep-th server). Therefore the calculations are preliminary and will remain unpublished; they are intended as reference for people who encounter similar mathematical problems.