The point-charge self-energy in Lee-Wick Theories

In this paper we study the ultraviolet and infrared behaviour of the self energy of a point-like charge in the vector and scalar Lee-Wick electrodynamics in a $d+1$ dimensional space time. It is shown that in the vector case, the self energy is strictly ultraviolet finite up to $d=3$ spatial dimensions, finite in the renormalized sense for any $d$ odd, infrared divergent for $d=2$ and ultraviolet divergent for $d>2$ even. On the other hand, in the scalar case, the self energy is striclty finite for $d\leq 3$, and finite, in the renormalized sense, for any $d$ odd.