Patrizia Vitale - Noncommutative U(1) gauge theory in the semiclassical limit

This talk was part of the Workshop on "Exactly Solvable Models" held at the ESI July 24 -- 26, 2024.
I will discuss U(1) gauge theory on Poisson manifolds as semiclassical limit of fully noncommutative spacetimes. The gauge potentials of Poisson electrodynamics are described as sections of a symplectic realization of the spacetime manifold and infinitesimal gauge transformations as a representation of the associated Lie algebroid acting on the symplectic realization. Finite gauge transformations are obtained by integrating the sections of the Lie algebroid to bisections of a symplectic groupoid, which form a one-parameter group of transformations