Reducible systems and embedding procedures in the canonical formalism

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 to isolate as in the Dirac approach, the independent subset of constraints or to introduce, as in the symplectic analysis, a series of Lagrange multipliers-for-Lagrange multipliers. 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 detail. (C) 1998 Academic Press.