The validity of dimensional regularization method on fractal spacetime (Q1789846)

Summary: \textit{K. Snozil} [``Quantum field theory on fractal spacetime: a new regularisation method'', J. Phys. A, Math. Gen. 20, No. 12, 3861--3875 (1987; \url{doi:10.1088/0305-4470/20/12/033})] developed a regularization method for quantum field theory on fractal spacetime. 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.