Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups

摘要

We develop a pseudo-differential Weyl calculus on nilpotent Lie groups whichallows one to deal with magnetic perturbations of right invariant vectorfields. For this purpose we investigate an infinite-dimensional Lie groupconstructed as the semidirect product of a nilpotent Lie grup and anappropriate function space thereon. We single out an appropriate coadjointorbit in the semidirect product and construct our pseudo-differential calculusas a Weyl quantization of that orbit.