Canad. J. Math. 65(2013), 1164-1200
Printed: Oct 2013
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.
field theory, fiber bundles, multisymplectic geometry, Hamiltonian systems
70S05 - Lagrangian formalism and Hamiltonian formalism
70S10 - Symmetries and conservation laws
53C80 - Applications to physics