Strict deformation quantization for a particle in a magnetic field

Recently, we introduced a mathematical framework for the quantization of a particle in a variable magnetic field. It consists in a modified form of the Weyl pseudodifferential calculus and a $C*$-algebraic setting, these two points of view being isomorphic in a suitable sense. In the present paper we leave Planck’s constant vary, showing that one gets a strict deformation quantization in the sense of Rieffel. In the limit $ℏ→0$ one recovers a Poisson algebra induced by a symplectic form defined in terms of the magnetic field.