2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/204624We 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.Mathematical PhysicsHigh Energy Physics - TheoryQuantum Physicstext