Construction of Lagrangian local symmetries for general quadratic theory

TL;DR

This paper presents a systematic method to construct local symmetry generators for general quadratic Lagrangian theories using Dirac formalism, avoiding the need to separate constraints into classes or choose a basis.

Contribution

It introduces a recurrence relation-based procedure for constructing symmetry generators directly from initial variables in quadratic theories.

Findings

Recurrence relations for symmetry generators are derived.

The method does not require separating constraints into first and second class.

Applicable directly to initial variables without basis choice.

Abstract

We propose a procedure which allows one to construct local symmetry generators of general quadratic Lagrangian theory. Manifest recurrence relations for generators in terms of so-called structure matrices of the Dirac formalism are obtained. The procedure fulfilled in terms of initial variables of the theory, and do not implies either separation of constraints on first and second class subsets or any other choice of basis for constraints.