On Covariant Phase Space and the Variational Bicomplex |
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Authors: | Enrique G Reyes |
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Affiliation: | (1) Departamento de Matemáticas y Ciencias de la Computación, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile |
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Abstract: | The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation. |
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Keywords: | symplectic geometry covariant phase space space of motions geometry of differential equations variational bicomplex Monge– Ampere equation |
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