Classical Geometric Interaction- picture-like Description

TL;DR

This paper proposes a classical geometric framework analogous to the quantum interaction picture, replacing phase space with solution spaces and detailing how to measure observables within this scheme.

Contribution

It introduces a novel classical geometric approach that parallels the quantum interaction picture using solution spaces instead of phase space.

Findings

A new classical geometric scheme for describing interactions.

Methodology for measuring observables in the proposed scheme.

Bridging classical and quantum geometric descriptions.

Abstract

In order to get the classical analogue of quantum interaction picture in classical symplectic geometric description, the space of solutions of free equations of motion is suggested to replace the phase space in $T^{*}Q$ description or the space of motions in usual classical symplectic geometric description. The way to determine measured values of observables in this scheme is worked out.