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The notion of observable in the covariant Hamiltonian formalism for the calculus of variations with several variables

Frederic Helein·Joseph Kouneiher
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Abstract

This papers is concerned with multisymplectic formalisms which are the frameworks for Hamiltonian theories for fields theory. Our main purpose is to study the observable $(n-1)$-forms which allows one to construct observable functionals on the set of solutions of the Hamilton equations by integration. We develop here two different points of view: generalizing the law $\{p,q\} = 1$ or the law $dF/dt = \{H,F\}$. This leads to two possible definitions; we explore the relationships and the differences between these two concepts. We show that -- in contrast with the de Donder--Weyl theory -- the two definitions coincides in the Lepage--Dedecker theory.

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Frederic Helein, Joseph Kouneiher. 2004-01-27. The notion of observable in the covariant Hamiltonian formalism for the calculus of variations with several variables. https://arxiv.org/abs/math-ph/0401047

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