Strict Deformation Quantization for a Particle in a Magnetic Field

Abstract

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 h --> 0 one recovers a Poisson algebra induced by a symplectic form defined in terms of the magnetic field.