Poisson–Poincaré reduction for Field Theories



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Berbel, M. A. and Castrillón López, Marco (2022) Poisson–Poincaré reduction for Field Theories. (Unpublished)

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Given a Hamiltonian system on a fiber bundle, there is a Poisson covariant formulation of the Hamilton equations. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, we study the reduction of this formulation to obtain an analogue of Poisson–Poincaré reduction for field theories. This procedure is related to the Lagrange–Poincaré reduction for field theories via a Legendre transformation. Finally, an application to a model of a charged strand evolving in an electric field is given.

Item Type:Article
Uncontrolled Keywords:Field theory; Symmetries; Covariant reduction; Poisson bracket; Polysymplectic; Multisymplectic; Poisson–Poincaré
Subjects:Sciences > Physics > Mathematical physics
ID Code:75599
Deposited On:18 Nov 2022 15:46
Last Modified:21 Nov 2022 08:15

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