Stochastic perturbation theory: A prequel to the reptation quantum Monte Carlo method

Abstract

I present a different approach to Rayleigh-Schr\"odinger perturbation theory, based on Laplace transforms and polynomial theory, yielding an iterative expression for the perturbative expansion of the energy of the nondegenerate ground state of a quantum system, which easily lends itself to symbolic computation. A stochastic interpretation of the various perturbative corrections naturally leads to a resummation scheme that is equivalent to the reptation quantum Monte Carlo method and that actually provided the original motivation to its development in the late 1990s.