Marius M\u antoiu and Radu Purice
Strict Deformation Quantization for
a Particle in a Variable Magnetic Field
(450K, Postscript)
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.