Misc,
Secondary Calculus and the Covariant Phase Space
(2008)
Abstract
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 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 re derive the existence of a Lie bracket among gauge invariant functions on the covariant phase space.
