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 jet spaces and (A. M. Vinogradov's) 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.

Secondary Calculus and the Covariant Phase Space

VITAGLIANO, LUCA
2009-01-01

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" 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 jet spaces and (A. M. Vinogradov's) 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1954125
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