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The validity of dimensional regularization method on fractal spacetime. (English) Zbl 1397.28003

Summary: K. Snozil [“Quantum field theory on fractal spacetime: a new regularisation method”, J. Phys. A, Math. Gen. 20, No. 12, 3861–3875 (1987; 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.

MSC:

28A80 Fractals
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