New Application of Functional Integrals to Classical Mechanics

TL;DR

This paper introduces a novel functional integral approach to classical mechanics by reformulating the Liouville equation using bosonic operators, leading to exactly solvable integrals for integrable systems.

Contribution

It presents a new class of functional integrals for classical dynamics based on bosonic operators and coherent states, expanding analytical tools for classical systems.

Findings

New functional integral representation for classical dynamics

Exact solutions for integrable systems

Reformulation of Liouville equation using bosonic operators

Abstract

In this paper a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of functional integrals for dynamical quantities in the coherent states representation. This results in a new class of functional integrals which are exactly solvable and can be found explicitly when the underlying classical systems are integrable.