$L_\infty$-algebra of braided electrodynamics

Marija Dimitrijević Ćirić; Nikola Konjik; Voja Radovanović; Richard J. Szabo; Miša Toman

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arXiv · 2204.06448

$L_\infty$-algebra of braided electrodynamics

Marija Dimitrijević Ćirić·Nikola Konjik·Voja Radovanović·Richard J. Szabo·Miša Toman

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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 deformation 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.

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Marija Dimitrijević Ćirić, Nikola Konjik, Voja Radovanović, Richard J. Szabo, Miša Toman. 2022-04-13. $L_\infty$-algebra of braided electrodynamics. https://arxiv.org/abs/2204.06448

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