Star-product in the presence of a monopole

Abstract

We present a deformed ⋆-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization–dequantization scheme, with the correspondence between classical observables and operators defined with the help of a quaternionic Hilbert space, following work by Emch and Jadczyk. The resulting product is well defined for a large class of complex functions and reproduces (at first order in ℏ) the Poisson structure of the particle in the monopole field. The product is associative only for quantized monopole charges, thus incorporating Dirac's quantization requirement.