Systematically Accelerated Convergence of Path Integrals

TL;DR

This paper introduces an analytical method that accelerates the convergence of path integrals in discretized theories, enabling more efficient calculations of continuum amplitudes with higher-order effective actions.

Contribution

The authors develop a systematic approach to improve path integral convergence, deriving effective actions up to order 9 that converge as 1/N^p, verified through Monte Carlo simulations.

Findings

Derived effective actions up to p=9 with improved convergence rates.

Validated the method through Monte Carlo simulations on various models.

Achieved convergence to continuum amplitudes faster than traditional methods.

Abstract

We present a new analytical method that systematically improves the convergence of path integrals of a generic $N$-fold discretized theory. Using it we calculate the effective actions $S^{(p)}$ for $p\le 9$ which lead to the same continuum amplitudes as the starting action, but that converge to that continuum limit as $1/N^p$. We checked this derived speedup in convergence by performing Monte Carlo simulations on several different models.