Recursive Construction of Generator for Lagrangian Gauge Symmetries

TL;DR

This paper develops recursive methods to construct local gauge symmetry transformations for certain Hamiltonian systems, including complex models like the Nambu-Goto string, enhancing understanding of gauge symmetries.

Contribution

It introduces recursive relations for constructing gauge symmetries in Hamiltonian systems with specific structure functions, extending previous approaches to more complex models.

Findings

Derived recursive relations for gauge transformations

Applied method to a system with primary and secondary constraints

Successfully constructed symmetries for a Nambu-Goto type system

Abstract

We obtain, for a subclass of structure functions characterizing a first class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge parameters. We apply this to a non-trivial Hamiltonian system involving two primary constraints, as well as two secondary constraints of the Nambu-Goto type.