The research program of Stochastic Deformation (with a view toward Geometric Mechanics)

TL;DR

This paper overviews a program of Stochastic Deformation applied to Classical Mechanics and Variational Calculus, inspired by quantization methods, aiming to bridge stochastic processes with geometric mechanics.

Contribution

It introduces a novel framework for stochastic deformation in classical mechanics, inspired by quantization, expanding the mathematical tools for geometric mechanics.

Findings

Proposes a new stochastic deformation approach.

Connects stochastic processes with geometric mechanics.

Provides foundational insights for future research.

Abstract

We give an overview of a program of Stochastic Deformation of Classical Mechanics and the Calculus of Variations, strongly inspired by the quantization method.