Partial Differential Hamiltonian Systems

Abstract We define partial differential (PD in the following), i.e., field theoretic analogues ofHamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, 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.