https://doi.org/10.1140/epjc/s10052-016-4566-y
Regular Article - Theoretical Physics
Physical model of dimensional regularization
Lexington, MA, 02420, USA
* e-mail: jschonfeld@aya.yale.edu
Received:
16
June
2016
Accepted:
17
November
2016
Published online:
24
December
2016
We explicitly construct fractals of dimension 
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 non-scalar fields, and speculate about implications for quantum gravity.
© The Author(s), 2016
