Partial Differential Hamiltonian Systems

Vitagliano, Luca

Canadian journal of mathematics, Tome 65 (2013) no. 5, pp. 1164-1200

Résumé

We define partial differential ( $\text{PD}$ in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, $\text{PD}$ Hamilton equations, $\text{PD}$ Noether theorem, $\text{PD}$ Poisson bracket, etc. Unlike the standard multisymplectic approach to Hamiltonian field theory, in our formalism, the geometric structure (kinematics) and the dynamical information on the “phase space” appear as just different components of one single geometric object.

Détail

DOI : 10.4153/CJM-2012-055-0

Mots-clés : 70S05, 70S10, 53C80, field theory, fiber bundles, multisymplectic geometry, Hamiltonian systems

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