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

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.

References in corpus (3)

• Time and M-theory
• Alternative linear structures for classical and quantum systems
• Quantum mechanics as a spontaneously broken gauge theory on a U(1) gerbe