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Generalization of Euler's Summation Formula to Path Integrals

Aleksandar Bogojevic·Antun Balaz·Aleksandar Belic
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Abstract

A recently developed analytical method for systematic improvement of the convergence of path integrals is used to derive a generalization of Euler's summation formula for path integrals. The first $p$ terms in this formula improve convergence of path integrals to the continuum limit from 1/N to $1/N^p$, where $N$ is the coarseness of the discretization. Monte Carlo simulations performed on several different models show that the analytically derived speedup holds.

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Aleksandar Bogojevic, Antun Balaz, Aleksandar Belic. 2005-09-16. Generalization of Euler's Summation Formula to Path Integrals. https://doi.org/10.1016/j.physleta.2005.06.053

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