Particle Mechanics Models with W-symmetries

TL;DR

This paper develops particle mechanics models with W-symmetries by employing Sp(2M) gauge invariance and partial gauge-fixings, leading to models invariant under diffeomorphisms and non-linear W-transformations, with applications to integrable systems.

Contribution

It introduces a novel class of particle mechanics models with W-symmetries derived from Sp(2M) gauge invariance and explores their gauge fixing and residual symmetries.

Findings

Models exhibit invariance under diffeomorphisms and W-transformations.

Lax operators are derived from equations of motion for matter variables.

Detailed examples demonstrate the models' structure and symmetry properties.

Abstract

We introduce a particle mechanics model with Sp($2M$) gauge invariance. Different partial gauge-fixings by means of sl(2) embeddings on the gauge algebra lead to reduced models which are invariant under diffeomorphisms and classical non-linear \W-transformations as the residual gauge symmetries thus providing a set of models of gauge and matter fields coupled in a \W-invariant way. The equations of motion for the matter variables give Lax operators in a matrix form. We examine several examples in detail and discuss the issue of integration of infinitesimal \W-transformations.