English

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}
}