Symplectic groupoids and Poisson electrodynamics

Vladislav G. Kupriyanov*, Alexey A. Sharapov, Richard J. Szabo

*Corresponding author for this work

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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.

Original languageEnglish
Article number39
JournalJournal of High Energy Physics
Issue number3
Publication statusPublished - 7 Mar 2024


  • Gauge Symmetry
  • Non-Commutative Geometry

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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