2023/08/14 by Vladislav Kupriyanov, Kupriyanov, Vladislav G., Alexey Sharapov +3 · 5 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #Quantum Electrodynamics and Casimir Effect #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2308.07406
openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative U(1) gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we interpret as the classical phase space of a point particle on noncommutative spacetime. In this picture gauge fields arise as bisections of the symplectic groupoid while gauge transformations are parameterized by Lagrangian bisections. We provide a geometric construction of a gauge invariant action functional which minimally couples a dynamical charged particle to a background electromagnetic field. Our constructions are elucidated by several explicit examples, demonstrating the appearances of curved and even compact momentum spaces, the interplay between gauge transformations and spacetime diffeomorphisms, as well as emergent gravity phenomena.