Path integration of a general two time action involving local and nonlocal harmonic oscillator potentials

Abstract

Path integration of a general two-time quadratic action having local and nonlocal harmonic oscillator potentials is performed within the framework of Feynman's polygonal path approach. The propagator (or the density matrix) thus obtained is diagonalized and the values of energies and eigenfunctions of a large number of states as a function of the strength of the nonlocal potential which simulates the effect of the medium on the solute represented by the local harmonic oscillator potential are derived. These values are used to calculate the effect of the solvent on the various properties of the solute. The possibility of representing the propagator in terms of an effective local action is also explored.