Abelian Subset of Second Class Constraints

TL;DR

This paper demonstrates that a specific mapping of second class constraints can produce a subset of abelian first class constraints, revealing a new structure within the constraint algebra using the most general Poisson framework.

Contribution

It introduces a novel mapping of second class constraints to abelian first class constraints and redefines constraints to achieve a symplectic algebra, generalizing previous approaches.

Findings

Half of the second class constraints form abelian first class constraints after mapping.

The explicit form of the mapping is derived considering the most general Poisson structure.

A redefinition of constraints makes their algebra symplectic.

Abstract

We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most general Poisson structure. We also introduce a proper redefinition of second class constraints that makes their algebra symplectic.