A quaternion based star product for a particle in the presence of a monopole

We present a deformed star product for a particle in the presence of magnetic monopole. The product is obtained within a Weyl quantization-dequantization scheme, with a correspondence between classical observables and operators on a quaternionic Hilbert space following work of Emch and Jadczyk. The resulting product among complex valued functions is well defined for a large class of functions and reproduces (at first order in h bar) the Poisson structure of the particle in the monopole field. The product is associative only for quantized monopole charge, thus reproducing Dirac's quantization requirement.