Star-product in the presence of a monopole

Abstract

We present a deformed star-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 hbar) 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.

References in corpus (5)

• Star products, duality and double Lie algebras
• To be or not to be? Magnetic monopoles in non-abelian gauge theories
• Duality symmetry for star products
• Fourier analysis on the affine group, quantization and noncompact Connes geometries
• Monopole-based quantization: a programme

Cited by in corpus (8)

• Symplectic realisation of electric charge in fields of monopole distributions
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• Quaternionic electrodynamics
• Dirac's monopole, quaternions, and the Zassenhaus formula
• Dirac's magnetic monopole and the Kontsevich star product
• The Kirillov picture for the Wigner particle
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• Charged Particle Motion in Spherically Symmetric Distributions of Magnetic Monopoles