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.
Categories: math-ph math.MP