On the Feynman path integral for the magnetic Schrödinger equation with a polynomially growing electromagnetic potential

Abstract

The Feynman path integrals for the magnetic Schrödinger equations are defined mathematically, in particular, with polynomially growing potentials in the spatial direction. For example, we can handle electromagnetic potentials [Formula: see text] such that [Formula: see text] “a polynomial of degree [Formula: see text] in [Formula: see text]” [Formula: see text] and [Formula: see text] are polynomials of degree [Formula: see text] in [Formula: see text]. The Feynman path integrals are defined as [Formula: see text]-valued continuous functions with respect to the time variable.