The Feynman-Kac-Ito formula for an infinite-dimensional Schrödinger equation with scalar and vector potentials

We consider an infinite-dimensional Schrödinger equation with scalar and vector potentials in a Hilbert space. The vector potential plays the same role as a magnetic field in the finite-dimensional case. We have proved the existence of the solution to the Cauchy problem. The solution is local in time and space variables and is expressed by a probabilistic formula of Feynman–Kac–Ito type.