Existence of real time quantum path integrals

Many interesting physical theories have analytic classical actions. We show how Feynman’s path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. start by introducing class of smooth regulators which render interference integrals absolutely convergent and thus unambiguous. The analyticity the allows us use Cauchy’s theorem deform integration domain onto set relevant, complex “thimbles” (or generalized steepest descent contours) each associated with saddle. regulator can then removed obtain an exact, non-perturbative representation. why usual method gradient flow, used identify relevant saddles finite-dimensional oscillatory integrals, fails in infinite-dimensional case. For troublesome high frequency modes, we replace it call “eigenflow” employ infinite-dimensional, “eigenthimble” over real time is convergent. bound modes corresponding Wiener measure free particle. Using dominated convergence infer that interacting defines good measure. While more intricate than its Euclidean counterpart, superior several respects. It seems particularly well-suited as quantum gravity where theory well developed but does not exist.