On Using the Quantum Mechanical Path Integral in Quantum Field Theory

Abstract

It is shown how matrix elements of the form 〈 x | e − iHt | y 〉, which arise in closed-form expressions for the generating functional, can he evaluated perturbatively using a path integral encountered in the quantum mechanics of a single particle. This allows one to compute Green′s functions without ever having to evaluate loop-momentum integrals. This technique is illustrated by considering, in the context of operator regularization. the vacuum polarization in scalar and spinor electrodynamics to one-loop order, the two-point function in φ 3 6 theory to two-loop order, the spinor self-energy in massless electrodynamics to one-loop order, the two-point function in Yang-Mills theory to one-loop order and the three-point function in axial electrodynamics to one-loop order.