2008/09/30 by L. Vitagliano
Mathematics · Physics and Astronomy · #math.DG #gr-qc #hep-th #math-ph #math.MP #msc:53C80 #msc:57R99 #msc:70S05
paper · pdf · doi:10.1016/j.geomphys.2008.12.001
published as J. Geom. Phys. 59 (2009) 426-447 · 40 pages, typos corrected
arxiv created 2010/05/04 · arxiv updated 2010/05/05
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.