Twisted Crossed Products and Magnetic Pseudodifferential Operators

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 (positions and magnetic momenta) with highly non-trivial commutation relations. On the algebraic side, the dynamical system is twisted by a cocyle 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 field.

27 pages

Cited by in corpus (11)

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• Analysis on singular spaces: Lie manifolds and operator algebras
• Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields
• Hölder Continuity of the Spectra for Aperiodic Hamiltonians
• A Calculus for Magnetic Pseudodifferential Super Operators
• Positive Quantization in the Presence of a Variable Magnetic Field
• The harmonic oscillator on the Moyal-Groenewold plane: an approach via Lie groups and twisted Weyl tuples