L . Vitagliano
نویسنده
چکیده
The covariant phase space of a lagrangian ¦eld theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a lagrangian ¦eld theory. Indeed, it is manifestly covariant and possesses a canonical (functional) ¤presymplectic structure¥ ω (as ¦rst 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.
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