Quark-antiquark pair production in space-time dependent fields

TL;DR

This paper develops a comprehensive framework for calculating fermion-antifermion pair production in space-time dependent classical fields, with applications to ultrarelativistic heavy-ion collisions, emphasizing gauge invariance and various approximation schemes.

Contribution

It introduces a method to compute pair production using retarded and advanced propagators, including gauge invariance considerations and boost-invariant approximations.

Findings

Derived all-order solutions for Dirac Green's functions in classical fields.

Analyzed gauge invariance of pair production expectation values.

Applied the framework to a boost-invariant model field.

Abstract

Fermion-antifermion pair-production in the presence of classical fields is described based on the retarded and advanced fermion propagators. They are obtained by solving the equation of motion for the Dirac Green's functions with the respective boundary conditions to all orders in the field. Subsequently, various approximation schemes fit for different field configurations are explained. This includes longitudinally boost-invariant forms. Those occur frequently in the description of ultrarelativistic heavy-ion collisions in the semiclassical limit. As a next step, the gauge invariance of the expression for the expectation value of the number of produced fermion-antifermion pairs as a functional of said propagators is investigated in detail. Finally, the calculations are carried out for a longitudinally boost-invariant model-field, taking care of the last issue, especially.