$L_\infty$-algebra of braided electrodynamics
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2022
- DOI:
- 10.48550/arXiv.2204.06448
- arXiv:
- arXiv:2204.06448
- Bibcode:
- 2022arXiv220406448D
- Keywords:
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- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Quantum Algebra
- E-Print:
- 16 pages