04-76 Marius Mantoiu, Radu Purice, Serge Richard

Twisted Crossed Products and Magnetic Pseudodifferential Operators (657K, Postscript) Mar 11, 04

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Abstract. There is a connection between the Weyl pseudodifferential calculus and crossed product C*-algebras associated with certain dynamical systems. And in fact both topics are involved in the quantization of a non-relativistic particle moving in R^n. Our paper studies the situation in which a variable magnetic field is also present. The Weyl calculus has to be modified, giving a functional calculus for a family of operators (position and magnetic momenta) with highly non-trivial commutation relations. On the algebraic side, the dynamical system is twisted by a cocycle defined by the flux of the magnetic field, leading thus to twisted crossed products. We outline the interplay between the modified pseudodifferential setting and the C*-algebraic formalism at an abstract level as well as in connection with magnetic fields.

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