A New Method for the Calculation of Functional and Path Integrals

TL;DR

This paper introduces a finite-element based method for calculating functional integrals, enhancing robustness and versatility, and enabling complex computations across various scientific disciplines.

Contribution

It presents a novel finite-element formulation for functional integrals, leveraging existing engineering tools for broader applicability and improved computational capabilities.

Findings

More robust and versatile calculation method

Enables study of previously intractable problems

Utilizes existing element libraries and shape functions

Abstract

Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a finite-element formulation. This approach is far more robust, versatile, and powerful than existing methods, thus allowing for more sophisticated computations and the study of problems that could not previously be tackled. Importantly, existing procedures, element libraries and shape functions, which have been developed throughout the years in the context of engineering analysis and partial differential equations, may be directly employed for this purpose.