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August 2004 The Notion of Observable in the Covariant Hamiltonian Formalism for the Calculus of Variations with Several Variables
Frederic Helein, Joseph Kouneiher
Adv. Theor. Math. Phys. 8(4): 735-777 (August 2004).

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. "The Notion of Observable in the Covariant Hamiltonian Formalism for the Calculus of Variations with Several Variables." Adv. Theor. Math. Phys. 8 (4) 735 - 777, August 2004.

Information

Published: August 2004
First available in Project Euclid: 2 June 2005

zbMATH: 1113.70023
MathSciNet: MR2141500

Rights: Copyright © 2004 International Press of Boston

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Vol.8 • No. 4 • August 2004
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