On using the quantum mechanical path integral in quantum field theory (Q1207163)

It is shown how matrix elements of the form \(\langle x| e^{- iHt}| y\rangle\), which arise in closed-form expressions for the generating functional, can be 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 \(\phi^ 3_ 6\) 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.