Feynman Integrals as Hida Distributions: the Case of Non-perturbative Potentials Dedicated to Jean-michel Bismut as a Small Token of Appreciation

are commonplace in physics and meaningless mathematically as they stand. Within white noise analysis [1, 2, 9, 10, 12, 14, 15, 16, 17] the concept of integral has a natural extension in the dual pairing of generalized and test functions and allows for the construction of generalized functions (the ”Feynman integrands”) for various classes of interaction potentials V , see e.g. [4, 5, 7, 10, 11, 13, 17], all of them by perturbative methods. This work extends this framework to the case where these fail, using complex scaling as in [6], see also [3]. In Section 2 we characterize Hida distributions. In Section 3 the U-functional is constructed, see Theorem 3.3. We prove in Section 4 that we obtain a solution of the Schroedinger equation, see Theorem 4.4. The strategy for a general construction of the Feynman integrand is provided in Section 5. Examples are given in Section 6.