Twistor integral representations of fundamental solutions of massless field equations

Abstract

We consider the general dimensional (complex) Minkowski spaces and the extended twistor spaces. We show that the fundamental solutions of the complex wave or Laplace equations are explicitly represented by the integrals of some closed forms on the twistor spaces. The closed form is defined from labeled trees explained in graphs theory, and is written, as the cohomology class, by the linear combination of the logrithmic forms on some hyperplane configuration complement in some complex affine space.