Constraint Algebras in Gauge Invariant Systems

TL;DR

This paper develops a Hamiltonian framework for gauge-invariant systems with complex local symmetries, explicitly deriving the constraint algebra and proving it to be first class, which is fundamental for understanding their structure.

Contribution

It introduces a Hamiltonian description for systems with higher-order local symmetries and explicitly computes their constraint algebra, demonstrating it is first class.

Findings

Constraint algebra is explicitly derived.

Constraint algebra is proven to be first class.

Framework applies to systems with derivatives of gauge parameters.

Abstract

The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and constraints with each other and with arbitrary function are explicitly obtained. The constraint algebra is proved to be the first class.