On Abelianization of First Class Constraints

TL;DR

This paper develops a systematic method to convert first class constraints into Abelian form using Dirac transformations, involving a matrix representation that simplifies the problem to solving linear differential equations.

Contribution

It introduces a new matrix representation for Abelianization of first class constraints, reducing the problem to solving linear differential equations.

Findings

Matrix representation facilitates Abelianization process

Method simplifies the transformation to linear differential equations

Provides a systematic approach for constraint Abelianization

Abstract

The systematic method for the conversion of first class constraints to the equivalent set of Abelian one based on the Dirac equivalence transformation is developed. The representation for the corresponding matrix performing this transformation is proposed. This representation allows one to lead the problem of abelianization to the solution of a certain system of first order {\it linear } differential equations for matrix elements .