Light-Cone Expansion of the Dirac Sea in the Presence of Chiral and Scalar Potentials

TL;DR

This paper develops a light-cone expansion method for analyzing the Dirac sea with external chiral and scalar potentials, providing a detailed perturbative framework for Green's functions and their causal structure.

Contribution

It introduces a novel light-cone expansion technique for the Dirac sea in the presence of chiral and scalar potentials, including a systematic summation of Feynman diagrams.

Findings

The Green's functions are expressed as an infinite sum of line integrals over potentials.

The Dirac sea decomposes into causal and non-causal parts, with the causal part exhibiting a light-cone expansion.

The non-causal contribution remains smooth and well-behaved in position space.

Abstract

We study the Dirac sea in the presence of external chiral and scalar/pseudoscalar potentials. In preparation, a method is developed for calculating the advanced and retarded Green's functions in an expansion around the light cone. For this, we first expand all Feynman diagrams and then explicitly sum up the perturbation series. The light-cone expansion expresses the Green's functions as an infinite sum of line integrals over the external potential and its partial derivatives. The Dirac sea is decomposed into a causal and a non-causal contribution. The causal contribution has a light-cone expansion which is closely related to the light-cone expansion of the Green's functions; it describes the singular behavior of the Dirac sea in terms of nested line integrals along the light cone. The non-causal contribution, on the other hand, is, to every order in perturbation theory, a smooth function in position space.