Stochastic perturbation theory: a prequel to Reptation Quantum Monte Carlo

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 non-degenerate 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 re-summation scheme that is equivalent to Reptation Quantum Monte Carlo and that actually provided the original motivation to its development in the late nineties.