(2009) Taneri, U.; Prykarpatsky, Y.; Vovk, M.; Prykarpatsky, A.
Based on analysis of reduced geometric structures on fi bered manifolds, invariant under action of an abelian functional symmetry group, we construct the symplectic structures associated with connection forms on the related principal fi ber bundles with abelian functional structure groups. The Marsden-Weinstein reduction procedure is applied to the Maxwell and Yang-Mills type dynamical systems. The geometric properties of Lorentz type constraints, describing the electromagnetic fi eld properties in vacuum and related
with the well known Dirac-Fock-Podolsky problem, are discussed.