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Partial Differential Hamiltonian Systems
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- Journal:
- Canadian Journal of Mathematics / Volume 65 / Issue 5 / 01 October 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1164-1200
- Print publication:
- 01 October 2013
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- Article
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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.
