The generalized canonical formalism for the electromagnetic field

The possibility of the Hamiltonian description of the electromagnetic field as a constrained dynamical system is analyzed. We use the BRST technique and we study the consequences of the implementation of a third order symmetry, that is a symmetry related to the symplectic group sp(3). The connection between this larger symmetry and the standard BRST one is also discussed. The following results are underlined: building a generalized BRST symmetry appears as possible; the standard and the sp(2) theories prove themselves as the first two stages of this global theory. By it, a more extended symmetry asks for a larger ghost spectrum and, so, more nonminimal terms can be employed in the gauge fixing procedure. (authors)