W$(2,4)$, Linear and Non-local \W-Algebras in Sp(4) Particle Model

TL;DR

This paper explores the relationships between different W-algebras, including linear, non-linear, and non-local types, within an Sp(4) particle model using Lax equations to understand their connections.

Contribution

It analyzes the connections between linear, non-linear, and non-local W-algebras in an Sp(4) particle model through Lax equations, highlighting their interrelations.

Findings

Relations between W_{2,4}^{linear} and W(2,4) algebras are clarified.

The role of the non-local V_{2,2} algebra is examined.

Insights into the algebraic structure of the Sp(4) particle model are provided.

Abstract

We comment on relations between the linear W_{2,4}^{linear} algebra and non-linear W(2,4)$ algebra appearing in a Sp(4) particle mechanics model by using Lax equations. The appearance of the non-local V_{2,2} algebra is also studied.