On the Weyl Representation of Metaplectic Operators
Symplectic Geometry
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller's formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder.
Cite
@article{arxiv.math/0503708,
title = {On the Weyl Representation of Metaplectic Operators},
author = {Maurice De Gosson},
journal= {arXiv preprint arXiv:math/0503708},
year = {2007}
}
Comments
To appear in Lett. Math. Physique