Covariant Supplementation Scheme for Infinitely Reducible First Class Constraints

TL;DR

This paper introduces a covariant scheme to convert infinitely reducible first class constraints into irreducible ones, simplifying the analysis of complex constrained dynamical systems in theoretical physics.

Contribution

It proposes a new covariant supplementation scheme applicable to a broad class of systems with complex constraints, including models like superstrings and superparticles.

Findings

Scheme successfully converts IR1C to irreducible constraints

Application to superstring and superparticle models demonstrates effectiveness

Provides modified Lagrangian formulations consistent with the scheme

Abstract

For a rather broad class of dynamical systems subject to mixed fermionic first and second class constraints or infinitely reducible first class constraints (IR1C), a manifestly covariant scheme of supplementation of IR1C to irreducible ones is proposed. For a model with IR1C only, an application of the scheme leads to a system with covariantly splitted and irreducible first and second class constraints. Modified Lagrangian formulations for the Green--Schwarz superstring, Casalbuoni--Brink--Schwarz superparticle and Siegel superparticle, which reproduce the supplementation scheme, are suggested.