A path integral leading to higher-order Lagrangians

TL;DR

This paper introduces a modification to phase-space path integrals that results in higher-order Lagrangians depending on accelerations in configuration space.

Contribution

It presents a novel modification of phase-space path integrals that yields higher-order Lagrangians involving accelerations.

Findings

Standard path integrals can be extended to produce higher-order Lagrangians.

The approach links phase-space modifications to new Lagrangian structures.

Potential implications for advanced classical and quantum theories.

Abstract

We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.