**DIPS 2/2008**[tex source, PostScript, PDF file, dvi]-
**Title:**Secondary Calculus and the Covariant Phase Space.**Author:**L. VitaglianoThe 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"

**ω**(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**ω**. As a byproduct we re derive the existence of a Lie bracket among gauge invariant functions on the covariant phase space.

See also arXiv: 0809.4164.

Last revised January 20, 2009. 36 pages, LaTeX-2e.

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