Research Article

The Validity of Dimensional Regularization Method on Fractal Spacetime

Figure 3

The fractal curve consists of the union , where . The dimension of fractal curve equals . Since is a fractal curve, the distance between points and cannot be measured using the Euclidean scale (ruler) ; otherwise, we will have or 0. However, the fractal curve can be measured using the nonlocal scale (ruler) ; for the way of measure see the formula (A.25).
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