Hamiltonian reduction in affine principal bundles

This paper presents a Hamiltonian reduction procedure for field theories over affine principal bundles introducing a canonical identification to describe the reduced multisymplectic space without the introduction of a connection. The main goal is to provide a Hamiltonian analogue of the Lagrangian reduction theory developed in [M. Castrillón López, P. M. Chacón and P. L. García, Lagrange–Poincaré reduction in affine principal bundles, J. Geom. Mech. 5(4) (2013) 399–414]. The core of this work lies in the derivation of this canonical identification, the reduced Hamilton–Cartan equations, and a reduced covariant bracket that describes the dynamics. Finally, this theoretical framework is illustrated with a fundamental example: molecular strands.