Remarks on Functional Integral Representations of Quantum Evolutions for Systems with Electromagnetic Fields

The solutions of Schrödinger equation in the form of the Dyson series are used as the starting point for functional integral representations of wave functions. Quantum systems in the presence of the external electromagnetic fields are discussed in this respect. The results on measure theoretic approach to functional integral representations of quantum states are proved and related to the appropriate mathematical formulations of Feynman path integrals.