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arXiv · 1612.03778

Physical model of dimensional regularization

Jonathan F. Schonfeld
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Abstract

We explicitly construct fractals of dimension 4-epsilon on which dimensional regularization approximates scalar-field-only quantum-field-theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and we argue that there probably is no Lorentz-invariant fractal of dimension greater than 2. We derive dimensional regularization's power-law screening first for fractals obtained by removing voids from 3-dimensional Euclidean space. The derivation applies techniques from elementary dielectric theory. Surprisingly, fractal geometry by itself does not guarantee the appropriate power-law behavior; boundary conditions at fractal voids also play an important role. We then extend the derivation to 4-dimensional Minkowski space. We comment on generalization to nonscalar fields, and speculate about implications for quantum gravity.

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Jonathan F. Schonfeld. 2016-12-03. Physical model of dimensional regularization. https://doi.org/10.1140/epjc%2Fs10052-016-4566-y

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