No Contact Terms for the Magnetic Field in Lorentz- and CPT-Violating   Electrodynamics
  In a Lorentz- and CPT-violating modification of electrodynamics, the fields of a moving charge are known to have unusual singularities. This raises the question of whether the singular behavior may include $\delta$-function contact terms, similar to those that appear in the fields of idealized dipoles. However, by calculating the magnetic field of an infinite straight wire in this theory, we demonstrate that there are no such contact terms in the magnetic field of a moving point charge 
Karl Schober and Brett Altschul
hep-th