THERMAL VACUUM POLARIZATION USING THE QUANTUM-MECHANICAL PATH-INTEGRAL

It has been shown how the quantum mechanical path integral can be used to do perturbative calculations in both quantum and thermal held theo ry to any order of the loop expansion. However, it is not readily appa rent how gauge invariance is made manifest in this approach; in this p aper we demonstrate how the vacuum polarization in electrodynamics at one-loop order is in fact transverse. We employ the one-dimensional Gr een's function G(tau,tau') = 1/2\tau-tau'\-1/2(tau+tau')+tau tau'/t in conjunction with an integration-by-parts procedure akin to that used by Strassler and Bern and Kosower. Surface terms in this approach are all sere. We obtain the high temperature expansion for the vacuum pola rization in the static limit.