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We present a new analytical method that systematically improves theconvergence of path integrals of a generic $N$-fold discretized theory. Usingit we calculate the effective actions $S^{(p)}$ for $p\le 9$ which lead to thesame continuum amplitudes as the starting action, but that converge to thatcontinuum limit as $1/N^p$. We checked this derived speedup in convergence byperforming Monte Carlo simulations on several different models.Comment: 4 pages, 1 figur

Systematically Accelerated Convergence of Path Integrals