Mercoledì 29 alle ore 15:00 in aula SP1L la Prof.ssa Patrizia Vitale (Università di Napoli Federico II) terrà un seminario nell’ambito del periodo intensivo INdAM “Poisson Geometry and Mathematical Physics” (https://sites.google.com/view/poisson2024/home). Seguono titolo e abstract.

TITLE: “Poisson Gauge Theory”

ABSTRACT
I shall discuss Abelian gauge theories on Poisson manifolds. The gauge potential one forms   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. A covariant electromagnetic two-form is obtained, together with a dual two-form, invariant under gauge transformations. The duality appearing in the picture originates from the existence of a pair of orthogonal foliations of the symplectic realization, which produce dual quotient manifolds, one related with space-time, the other with momenta.