Canonical Transformations and Hamiltonian Evolutionary Systems

Details Canonical Transformations and Hamiltonian Evolutionary Systems Canonical Transformations and Hamiltonian Evolutionary Systems

2005-01-21

arxiv.org/abs/math-ph/0501056v1

Physics

Mathematical Physics

14 pages

Scientific paper

In many Lagrangian field theories one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different cases. These three cases depend on the specific dimensions of the vector bundle of the theory and the associated Hamiltonian differential operator. We also show how a canonical transformation transforms a Hamiltonian evolutionary system and its conservation laws. Finally we illustrate these ideas with three examples.

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