A semiclassical constrained Hamiltonian system which was established to studydynamical systems of matrix valued non-Abelian gauge fields is employed toformulate spin Hall effect in noncommuting coordinates at the first order inthe constant noncommutativity parameter theta . The method is first illustratedby studying the Hall effect on the noncommutative plane in a gauge independentfashion. Then, the Drude model type and the Hall effect type formulations ofspin Hall effect are considered in noncommuting coordinates and \theta deformedspin Hall conductivities which they provide are acquired. It is shown that byadjusting \theta different formulations of spin Hall conductivity areaccomplished. Hence, the noncommutative theory can be envisaged as an effectivetheory which unifies different approaches to similar physical phenomena.
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