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Lie-Poisson gauge formalism provides a semiclassical description ofnoncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity.Using the Dirac approach to constrained Hamiltonian systems, we focus on aclass of Lie-Poisson gauge models, which exhibit an admissible Lagrangiandescription. The underlying noncommutativity is supposed to be purely spatial.Analysing the constraints, we demonstrate that these models have as manyphysical degrees of freedom as there are present in the Maxwell theory.

Hamiltonian analysis in Lie-Poisson gauge theory