Simplifying the algebra of first class constraints, examples on SO(3) and SO(4)

TL;DR

The paper presents a method to transform non-abelian first class constraint systems into abelian ones locally, using differential equations and regularization, with examples on SO(3) and SO(4).

Contribution

It introduces a novel approach to simplify non-abelian constraints by locally converting them into abelian constraints through differential equations.

Findings

Non-abelian systems can be locally abelianized.

Regularization is necessary for multiplicative constraints.

Examples on SO(3) and SO(4) demonstrate the method.

Abstract

We discuss the problem of non abelian constrained systems and the origin of appearance of non abelian algebras. We show that it is possible, in principle, to change a non abelian system to an abelian one, at least locally. Our method is based on solutions of the differential equations due to the algebra of first class constraints. We suggest that multiplicative constraints should be regularized at each step of calculation. Some examples on SO(3) and SO(4) algebras are discussed. We show that they can be replaced by abelian constraints.