Dimensional Reduction for Generalized Poisson Brackets

TL;DR

This paper explores how Hamiltonian systems with nonconstant Poisson brackets can be simplified through dimensional reduction, resulting in constant brackets, with theoretical insights and illustrative examples.

Contribution

It introduces a general theory for dimensional reduction of systems with nonconstant Poisson brackets, showing that reduced brackets become constant.

Findings

Reduced brackets are always constant after dimensional reduction.

Theoretical framework for systems with nonconstant Poisson brackets.

Examples illustrating the reduction process.

Abstract

We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets are always constant. Some examples are given alongside the general theory.