The Validity of Dimensional Regularization Method on Fractal Spacetime

Abstract

Svozil developed a regularization method for quantum field theory on fractal spacetime (1987). Such a method can be applied to the low-order perturbative renormalization of quantum electrodynamics but will depend on a conjectural integral formula on non-integer-dimensional topological spaces. The main purpose of this paper is to construct a fractal measure so as to guarantee the validity of the conjectural integral formula.