A FUNCTIONAL-APPROACH TO LOOP DIAGRAMS

A closed-form expression for the N-loop contribution to the generating functional can be written down using the heat kernel [x/e(-Ht)\y]. If H = 1/2(p - d A(x))(2) + V(x)(p = i partial derivative) where A(mu) a nd V are functions of the background field, then by using quantum-mech anical techniques, this heat kernel can be expanded in powers of the b ackground field, allowing one to compute Green's functions. We demonst rate that one can also employ to this end a distinct functional approa ch 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.