Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields

The extended phase space P for Yang-Mills and Dirac fields in the Minkowski space is a Sobolev space of Cauchy data. We prove in P the existence and uniqueness theorem for the evolution equations. We show that the Lie algebra gs(P) of infinitesimal gauge symmetries of P is a Hilbert-Lie algebra carrying a Beppo Levi topology. The connected group GS(P) of gauge symmetries of P with the Lie algebra gs(P) is a Hilbert-Lie group acting properly in P. We construct a closed connected subgroup GS(P)0 of GS(P), acting in P with a momentum map J0, such that the constraint equations are given by J0=0. The action of GS(P)0 in P is free and proper. (orig.)