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# Partial Differential Hamiltonian Systems

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Published:2012-12-29
Printed: Oct 2013
• Luca Vitagliano,
DipMat, University of Salerno, and Istituto Nazionale di Fisica Nucleare, GC Salerno, via Ponte don Melillo, 84084 Fisciano (SA) Italy
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## Abstract

We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in 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.
 Keywords: field theory, fiber bundles, multisymplectic geometry, Hamiltonian systems
 MSC Classifications: 70S05 - Lagrangian formalism and Hamiltonian formalism 70S10 - Symmetries and conservation laws 53C80 - Applications to physics

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