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

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 behavior of higher order Furry picture processes. Here, Fierz transformations of Volkov spinors are developed and applied to a first-order and a second-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.

Figure 1

Furry picture, one-vertex photon radiation.

Figure 2

Furry picture, two-vertex Compton scattering.

Figure 3

An $n$-vertex Furry picture process.