Wigner functions, Fresnel optics, and symplectic connections on phase space

Details Wigner functions, Fresnel optics, and symplectic connections on phase space Wigner functions, Fresnel optics, and symplectic connections on phase space

2007-10-18

arxiv.org/abs/0710.3544v1

Int.J.Geom.Meth.Mod.Phys.5:663-676,2008

Physics

Mathematical Physics

Scientific paper

10.1142/S0219887808003089

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.

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