  The Feynman path integrals for the magnetic Schroedinger equations are
defined mathematically, in particular, with polynomially growing potentials in
the spatial direction. For example, we can handle electromagnetic potentials
$(V,A_{1},A_{2},...,A_{d})$ such that $V(t,x) = |x|^{2(l+1)} + $`` a polynomial
of degree $(2l + 1)$ in $x$ " ($l = 0,1,2,...$) and $A_{j}(t,x)$ are
polynomials of degree $l$ in $x$. The Feynman path integrals are defined as
$L^2$-valued continuous functions with respect to the time variable.
