Poisson-Poincaré reduction for Field Theories

Abstract

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.

arXiv comment34 pages

References in corpus (13)

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• Multi-moment maps
• Closed forms and multi-moment maps
• Lagrange-Poincare field equations
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• $G$-Strands
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Cited by in corpus (2)

• Hamiltonian Reduction in Affine Principal Bundles
• Gauge reduction in covariant field theory