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Partial Differential Hamiltonian Systems

  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 field theory, fiber bundles, multisymplectic geometry, Hamiltonian systems
MSC Classifications: 70S05, 70S10, 53C80 show english descriptions Lagrangian formalism and Hamiltonian formalism
Symmetries and conservation laws
Applications to physics
70S05 - Lagrangian formalism and Hamiltonian formalism
70S10 - Symmetries and conservation laws
53C80 - Applications to physics
 

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