Gauge symmetry and W-algebra in higher derivative systems

TL;DR

This paper investigates gauge symmetry in higher derivative systems from a Hamiltonian perspective, revealing fewer gauge parameters than primary constraints and linking gauge symmetry to W-algebra in specific models.

Contribution

It clarifies the nature of gauge symmetry in higher derivative systems and establishes a connection to W-algebra in the context of the rigid relativistic particle.

Findings

Fewer gauge parameters than primary constraints in higher derivative systems

Established link between gauge symmetry and W-algebra in specific models

Illustrated concepts with examples including the rigid relativistic particle

Abstract

The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general {\it{less}} than the number of independent primary first class constraints, thereby distinguishing it from conventional first order systems. Different models have been considered as illustrative examples. In particular we show a direct connection between the gauge symmetry and the W-algebra for the rigid relativistic particle.