Some new techniques of path integration

Perturbation theory based on Feynman path integral provides a new technique of obtaining exact energy Green's function in a number of cases. It is shown that only the knowledge of the free particle propagator is sufficient for this purpose and no explicit path integration is involved. The possibility of summing the series in a closed form depends on an appropriate representation for the free particle, the energy dependent Green's function. The reason for this are explained on the basis of Hilbert-Schmidt analysis. This analysis provides a new insight on the perturbation method and an alternative approach for obtaining Green's function. For dealing with time-dependent potentials an alternative technique based on the existence of an invariant is presented. This reduces the original time-dependent problem to an associated time-independent one. The latter can then be treated by perturbation approach. (author). 41 refs