# Path integrals for higher derivative actions

## TL;DR

This paper develops methods for evaluating Euclidean path integrals involving higher derivative actions, which are relevant in physical models like stiff polymers and membranes, by relating them to Gaussian fields.

## Contribution

It introduces a systematic approach to compute higher derivative path integrals, extending existing techniques to more complex actions involving quadratic dependence on acceleration and velocity.

## Key findings

- Established a relation between higher derivative path integrals and Gaussian fields.
- Extended the method to evaluate even higher order path integrals.
- Applicable to models in polymer physics, membrane mechanics, and electrolyte systems.

## Abstract

We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with bending rigidity as well as a number of models for electrolytes. The approach used is based on the relation between quadratic path integrals and Gaussian fields and we also show how it can be extended to the evaluation of even higher order path integrals.