Fierz relations for Volkov spinors and the simplification of Furry picture traces

TL;DR

This paper introduces Fierz transformations for Volkov spinors to simplify trace calculations in strong field QED processes, enhancing theoretical analysis of Furry picture phenomena.

Contribution

It develops Fierz relations for Volkov spinors and demonstrates their application to simplify Furry picture trace calculations in strong field QED.

Findings

Fierz transformations significantly reduce calculation complexity.

Symmetry properties further simplify trace evaluations.

Applicable to both first and second order Furry picture processes.

Abstract

Transition probability calculations of strong field particle processes in the Furry picture, typically use fermion Volkov solutions. These solutions have a relatively complicated spinor due to the interaction of the electron spin with a strong external field, which in turn leads to unwieldy trace calculations. The simplification of these calculations would aid theoretical studies of strong field phenomena such as the predicted resonance behaviour of higher order Furry picture processes. Here, Fierz transformations of Volkov spinors are developed and applied to a 1st order and a 2nd order Furry picture process. Combined with symmetry properties, the techniques presented here are generally applicable and lead to considerable simplification of Furry picture analytic calculations.