  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.
