Reducible systems and embedding procedures in the canonical formalism

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.