QED amplitudes: recurrence relations to all orders

TL;DR

This paper derives all-order recurrence relations for QED amplitudes based on Feynman diagram construction, applicable to any loop order and external particle configuration, with connections to Schwinger-Dyson equations.

Contribution

It introduces a novel set of recurrence relations for QED amplitudes valid at all loop orders, expanding the tools for amplitude calculations.

Findings

Recurrence relations for QED amplitudes derived

Relations hold for all loop orders and external particle combinations

Connections established with Schwinger-Dyson equations

Abstract

We describe the origins of recurrence relations between field theory amplitudes in terms of the construction of Feynman diagrams. In application we derive recurrence relations for the amplitudes of QED which hold to all loop orders and for all combinations of external particles. These results may also be derived from the Schwinger-Dyson equations.