Article ID Journal Published Year Pages File Type
1895091 Journal of Geometry and Physics 2009 22 Pages PDF
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” ω (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 jet spaces and (A. M. Vinogradov’s) secondary calculus. In particular, we describe the degeneracy distribution of ω. As a byproduct we rederive the existence of a Lie bracket among gauge invariant functions on the covariant phase space.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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