Noncommutative U(1) Gauge Theory in the Semiclassical Limit

Explore U(1) gauge theory on Poisson manifolds as a semiclassical limit of fully noncommutative spacetimes in this 40-minute conference talk from the Workshop on "Exactly Solvable Models" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the intricacies of Poisson electrodynamics, where gauge potentials are described as sections of a symplectic realization of the spacetime manifold. Examine how infinitesimal gauge transformations are represented as actions of the associated Lie algebroid on the symplectic realization. Discover the process of obtaining finite gauge transformations by integrating sections of the Lie algebroid to bisections of a symplectic groupoid, forming a one-parameter group of transformations. Gain insights into this advanced topic in mathematical physics and its implications for understanding noncommutative gauge theories.