Conversion of second class constraints by deformation of Lagrangian local symmetries

TL;DR

This paper introduces a method to convert second class constraints into gauge symmetries through deformation of local symmetries in the Lagrangian, revealing hidden symmetries without changing the configuration space.

Contribution

It presents a novel procedure for converting second class constraints into gauge symmetries by deforming local symmetries, applicable without extending the configuration space.

Findings

Successfully applied to membrane theory with gauge degrees of freedom for metric components.

Revealed hidden symmetries in theories with non-linear realizations of global symmetries.

Applicable to various systems including classical mechanics, sigma-models, and vector field theories.

Abstract

For a theory with first and second class constraints, we propose a procedure for conversion of second class constraints based on deformation the structure of local symmetries of the Lagrangian formulation. It does not require extension or reduction of configuration space of the theory. We give examples in which the initial formulation implies a non linear realization of some global symmetries, therefore is not convenient. The conversion reveals hidden symmetry presented in the theory. The extra gauge freedom of conversed version is used to search for a parameterization which linearizes the equations of motion. We apply the above procedure to membrane theory (in the formulation with world-volume metric). In the resulting version, all the metric components are gauge degrees of freedom. The above procedure works also in a theory with only second class constraints presented. As an examples, we discuss arbitrary dynamical system of classical mechanics subject to kinematic constraints, O(N)-invariant nonlinear sigma-model, and the theory of massive vector field with Maxwell-Proca Lagrangian.