Asymptotic Properties of Path Integral Ideals

TL;DR

This paper introduces the concept of path integral ideals to analyze how discrete theories approach the continuum limit, identifying dominant terms that influence their asymptotic behavior and convergence.

Contribution

It presents a novel framework for understanding the flow of discrete theories to the continuum using path integral ideals and classifies this flow based on potential divergence.

Findings

Identifies dominant terms in effective potential for large time steps

Classifies flow behavior according to potential divergence

Enhances understanding of convergence in discrete theories

Abstract

We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of divergence of the potential at spatial infinity. Studying the asymptotic behavior of path integral ideals we isolate the dominant terms in the effective potential that determine the behavior of a generic theory for large discrete time steps.