Abelianization of First Class Constraints

TL;DR

This paper presents a method to transform non-abelian first class constraints into abelian ones using a projection map, facilitating easier gauge fixing in constrained Hamiltonian systems.

Contribution

It introduces an explicit projection map for irreducible first class constraints that achieves abelianization without requiring a closed algebra.

Findings

Explicit form of the projection map for irreducible constraints

Method to obtain gauge fixing conditions satisfying symplectic algebra

Demonstrates abelianization without algebra closure assumption

Abstract

We show that a given set of first class constraints becomes abelian if one maps each constraint to the surface of other constraints. There is no assumption that first class constraints satisfy a closed algebra. The explicit form of the projection map is obtained at least for irreducible first class constraints. Using this map we give a method to obtain gauge fixing conditions such that the set of abelian first class constraints and gauge fixing conditions satisfy the symplectic algebra.