Ervin Goldfain. On the Multifractal Description of Lagrangian Field Theory (first draft)
Submitted on: Dec 30, 2016, 10:53:22
Natural Sciences / Physics / Quantum field theory
Description: We show that the structure of effective field theories replicates the geometry of multifractal sets, which are built from the fundamental concepts of scales and measures. It is found that the Standard Model (SM) Lagrangian is characterized by a dominant generalized dimension D = 2, while the same dimension of Einstein-Hilbert Lagrangian turns out to be D = 4. On the one hand, this result disfavors any trivial unification of SM and General Relativity (GR) based on field theory. On the other, it hints that the continuous spectrum of dimensions between SM and GR may naturally account for the existence of non-baryonic Dark Matter.
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On the Multifractal Description of Lagrangian Field Theory.pdf