A finite model for electrodynamics by introducing a form factor fHD2(ℓ2□)=1+(-ℓ2□)2 into the kinetic term of Maxwell theory

In this paper, a higher-derivative model for electrodynamics is presented in a  D+1 dimensional Minkowski space-time by introducing a form factor into the kinetic term of Maxwell theory as -1/4µ0 FµνFµν→ -1/4µ0 FµνFHD2(ℓ2□)Fµν , where  is a characteristic length scale. Our calculations show that for DÊÎ{3, 4, 5} the electrostatic potential of a point charge is finite at the position of the point charge in this higher-derivative modification of Maxwell's theory. For D=3 the explicit form of the potential and the electric field of a point charge are obtained analytically in this higher-derivative electrodynamics. According to numerical estimations, the upper bound for the characteristic length scale ℓ is ℓmax ~1/100ℓelectroweak  , where ℓelectroweak= 10-18m is the electroweak length scale. Finally, it should be emphasized that for ℓ<<1 the results of this paper are compatible with the results of ordinary Maxwell theory.