On Hamilton–Poincaré field equations
Volume 110 / 2016
Banach Center Publications 110 (2016), 9-24
MSC: Primary 70S05, 70S10; Secondary 53C42.
DOI: 10.4064/bc110-0-1
Abstract
We introduce the prolongation, to the reduced extended multimomentum bundle, of a vertical vector field (in the total space of the corresponding configuration bundle) which is invariant under the action of the symmetry Lie group. Using this construction, we present a geometric description of the Hamilton–Poincaré field equations associated with a symmetric Hamiltonian field theory. Finally, we discuss an example: the theory of minimal submanifolds of a Riemannian manifold.
