Classification of constraints using chain by chain method

TL;DR

This paper presents the 'chain by chain' method for classifying and restructuring constraints in systems with mixed first and second class constraints, enabling clearer analysis of their algebraic properties.

Contribution

The paper introduces a novel 'chain by chain' approach that classifies constraints into irreducible chains and redefines second class constraints to achieve a symplectic algebra.

Findings

Constraints are classified into irreducible chains.

Second class constraints are redefined to form a symplectic algebra.

The method simplifies the analysis of constraint structures.

Abstract

We introduce "chain by chain" method for constructing the constraint structure of a system possessing both first and second class constraints. We show that the whole constraints can be classified into completely irreducible first or second class chains. We found appropriate redefinition of second class constraints to obtain a symplectic algebra among them.