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Finite dimesional Hamiltonian formalism for gauge and field theories

Frédéric Hélein·Joseph Kouneiher
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Abstract

We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized Poisson $\mathfrak{p}$-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of $\mathfrak{p}$-brackets. As illustration of our formalism we present three examples: the interacting scalar fields, conformal string theory and the electromagnetic field.

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Frédéric Hélein, Joseph Kouneiher. 2000-10-23. Finite dimesional Hamiltonian formalism for gauge and field theories. https://doi.org/10.1063/1.1467710

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