PoS - Proceedings of Science
Volume 406 - Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2021) - Workshop on New Developments in Quantum Gravity and String Theory
$L_\infty$-algebra and braided field theory
M. Dimitrijević Ćirić*, N. Konjik, V. Radovanović, R. Szabo and M. Toman
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Published on: November 23, 2022
Abstract
Using the recently developed formalism of braided noncommutative field theory, we construct an explicit example of braided electrodynamics, that is, a noncommutative $U(1)$ gauge theory coupled to a Dirac fermion. We construct the braided $L_\infty$-algebra of this field theory and apply the formalism to obtain the braided equations of motion, action functional and conserved matter current. The braided deformations leads to a modification of the charge conservation. Finally, the Feynman integral appearing in the one-loop contribution to the vacuum polarization diagram is calculated. There are no non-planar diagrams, but the UV/IR mixing appears nevertheless. We comment on this unexpected result.
DOI: https://doi.org/10.22323/1.406.0197
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