From Feynman-Kac formula to Feynman integrals via analytic continuation

By using a calculus based on Brownian bridge measures, it is shown that under mild assumptions on V (e.g. V is in the Kato class) the fundamental solution (FS) q (t,x,y) for the heat equation can be represented by the Feynman-Kac formula. Furthermore, it has an analytic continuation in t over +, where , and q([var epsilon] + it,x,y) can be expressed via Wiener path integrals. For small [var epsilon] > 0 it can be considered as an approximation of the FS for the Schrodinger equation . We also give an estimate of q(t,x,y) for t [set membership, variant] +.