Abstract
We introduce a class of pseudodifferential operators acting on functions defined on an arbitrary symplectic space (ℝ2n
, ω). These operators arise naturally when one considers the generalized commutation relations from non-commutative quantum mechanics. The connection with the usual Weyl operator
with symbol a is made using a family of intertwiners W
g
defined in terms of the cross-Wigner transform W(f, g). We show that if a belongs to some adequate Shubin symbol classes there is a simple relation between the eigenvalues of
and those of
.
AMS Subject Classifications::
Acknowledgements
This work has been financed by the Austrian Research Agency FWF (Project ‘Symplectic Geometry and Applications to TFA and QM’, Project number P20442-N13).