%0 Journal Article
%T Secondary Calculus and the Covariant Phase Space
%A L. Vitagliano
%J Mathematics
%D 2008
%I arXiv
%R 10.1016/j.geomphys.2008.12.001
%X The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w (as first noticed by Zuckerman in 1986) whose degeneracy (functional) distribution is naturally interpreted as the Lie algebra of gauge transformations. We propose a fully rigorous approach to the covariant phase space in the framework of secondary calculus. In particular we describe the degeneracy distribution of w. As a byproduct we rederive the existence of a Lie bracket among gauge invariant functions on the covariant phase space.
%U http://arxiv.org/abs/0809.4164v5