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.
Poisson–Poincaré reduction for field theories
Tipo de Actividad
Artículos en revistasISSN
0393-0440Palabras Clave
.Field theorySymmetriesCovariant bracketPolysymplecticMultisymplecticPoisson–Poincaré