Reducible systems and embedding procedures in the canonical formalism

TL;DR

This paper introduces a unified method for handling reducible constrained systems in the canonical formalism, simplifying the process by enlarging phase and configuration spaces and clarifying the connection between Dirac and symplectic approaches.

Contribution

It presents a systematic approach that avoids isolating independent constraints or adding multiple Lagrange multipliers, unifying Dirac and symplectic methods for reducible systems.

Findings

Unified treatment of reducible systems in Dirac and symplectic formalisms

Simplified analysis without isolating independent constraints

Detailed example with p-form gauge fields

Abstract

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not necessary, as in the Dirac approach, to isolate the independent subset of constraints or to introduce, as in the symplectic analysis, a series of lagrange multipliers-for-lagrange multipiers. This analysis illuminates the close connection between the Dirac and symplectic approaches of treating reducible theories, which is otherwise lacking. The example of p-form gauge fields (p=2,3) is analyzed in details.