*Published Paper*

**Inserted:** 5 dec 2023

**Last Updated:** 10 may 2024

**Journal:** Communications in Mathematical Physics

**Volume:** 377

**Pages:** 1461-1503

**Year:** 2020

**Doi:** 10.1007/s00220-020-03744-x

**Abstract:**

A Feynman path integral formula for the Schr\"odinger equation with magnetic field is rigorously mathematically realized in terms of infinite dimensional oscillatory integrals. We show (by the example of a linear vector potential) that the requirement of the independence of the integral on the approximation procedure forces the introduction of a counterterm to be added to the classical action functional. This provides a natural explanation for the appearance of a Stratonovich integral in the path integral formula for both the Schr\"odinger and heat equation with magnetic field.