New realizations of observables in dynamical systems with second class constraints

TL;DR

This paper introduces new realizations of the algebra of observables in constrained dynamical systems by constructing quotient algebras from the original Poisson algebra, providing explicit formulas for generators and brackets.

Contribution

It presents novel quotient algebra constructions for observables in systems with second class constraints, expanding the mathematical framework of Dirac brackets.

Findings

Explicit formulas for generators and brackets of new algebra realizations

Families of quotient algebras describing observables

Enhanced understanding of algebraic structures in constrained systems

Abstract

In the Dirac bracket approach to dynamical systems with second class constraints observables are represented by elements of a quotient Dirac bracket algebra. We describe families of new realizations of this algebra through quotients of the original Poisson algebra. Explicite expressions for generators and brackets of the algebras under consideration are found.