DIPS 2/2008 [tex source, PostScript, PDF file, dvi]

Title: Secondary Calculus and the Covariant Phase Space.

Author: L. Vitagliano

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" 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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