A functional approach to loop diagrams

Abstract

A closed-form expression for the N-loop contribution to the generating functional can be written down using the heat kernel [Formula: see text]. If [Formula: see text] where Aμ and V are functions of the background field, then by using quantum-mechanical techniques, this heat kernel can be expanded in powers of the background field, allowing one to compute Green's functions. We demonstrate that one can also employ to this end a distinct functional approach developed by Onofri, which circumvents both loop-momentum integrals and the quantum-mechanical path integral. We illustrate the technique by computing the two-point function in scalar electrodynamics to one-loop order.