04-396 Marius M\u antoiu and Radu Purice

Strict Deformation Quantization for a Particle in a Variable Magnetic Field (450K, Postscript) Nov 22, 04

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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 $\h\rightarrow 0$ one recovers a Poisson algebra induced by a symplectic form defined in terms of the magnetic field.

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