Jacobi Group Symmetry of Hamilton's Mechanics

TL;DR

This paper demonstrates that certain diffeomorphisms in an extended phase space preserve key geometric structures and satisfy Hamilton's equations up to canonical transformations, revealing a Jacobi group symmetry in Hamiltonian mechanics.

Contribution

It introduces a Jacobi group symmetry framework for Hamilton's mechanics by analyzing diffeomorphisms that preserve symplectic and orthogonal structures in extended phase space.

Findings

Diffeomorphisms preserve the symplectic 2-form and a degenerate orthogonal metric.

Hamilton's equations are satisfied up to canonical transformations.

The structure reveals a Jacobi group symmetry in Hamiltonian mechanics.

Abstract

We show that the diffeomorphisms of an extended phase space with time, energy, momentum and position degrees of freedom that leave invariant the symplectic 2-form and and a degenerate orthogonal metric dt^2 locally satisfy Hamilton's equations up to the usual canonical transformations on the position-momentum subspace.