Rigorous real-time Feynman path integral for vector potentials

In this paper, we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the L2 transition probability amplitude via improper Riemann integrals. Our formulation will hold for a vector potential Hamiltonian for which its potential and vector potential each carry at most a finite number of singularities and discontinuities. (author)