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Annals of Global Analysis and Geometry

, Volume 36, Issue 3, pp 293–322 | Cite as

Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups

  • Ingrid Beltiţă
  • Daniel BeltiţăEmail author
Original Paper

Abstract

We develop a pseudo-differential Weyl calculus on nilpotent Lie groups, which allows one to deal with magnetic perturbations of right invariant vector fields. For this purpose, we investigate an infinite-dimensional Lie group constructed as the semidirect product of a nilpotent Lie group and an appropriate function space thereon. We single out an appropriate coadjoint orbit in the semidirect product and construct our pseudo-differential calculus as a Weyl quantization of that orbit.

Keywords

Weyl calculus Magnetic field Lie group Semidirect product 

Mathematics Subject Classification (2000)

Primary 47G30 Secondary 22E25 22E65 35S05 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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