  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.
