A geometrical interpretation of classical W-transformations

TL;DR

This paper provides a straightforward geometric perspective on classical W-transformations, interpreting them as deformations of energy surfaces via canonical transformations in a two-dimensional phase space.

Contribution

It introduces a simple geometric interpretation of classical W-transformations as deformations of energy surfaces through canonical transformations.

Findings

W-transformations can be understood geometrically as surface deformations

Canonical transformations preserve phase space volume

The interpretation simplifies understanding of classical W-transformations

Abstract

We give a simple geometrical interpretation of classical $\W$-transformations as deformations of constant energy surfaces by canonical transformations on a two-dimensional phase space.