(L_\infty\)-algebra of braided electrodynamics

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 for...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Ćirić, Marija Dimitrijević, Konjik, Nikola, Radovanović, Voja, Szabo, Richard J, Toman, Miša
Format: Article
Language:English
Subjects:
Algebra
Braiding
Electrodynamics
Equations of motion
Fermions
Field theory
Formalism
Gauge theory
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Summary: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.
ISSN:2331-8422