Wigner functions, Fresnel optics, and symplectic connections on phase space
Mathematical Physics
2008-11-26 v1 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
We prove that Wigner functions contain a symplectic connection. The latter covariantises the symplectic exterior derivative on phase space. We analyse the role played by this connection and introduce the notion of local symplectic covariance of quantum-mechanical states. This latter symmetry is at work in the Schroedinger equation on phase space.
Keywords
Cite
@article{arxiv.0710.3544,
title = {Wigner functions, Fresnel optics, and symplectic connections on phase space},
author = {J. M. Isidro},
journal= {arXiv preprint arXiv:0710.3544},
year = {2008}
}