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

Understand

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.