Ervin Goldfain. On the Multifractal Description of Lagrangian Field Theory (updated draft)
Submitted on: Jan 22, 2017, 18:30:44
Natural Sciences / Physics / Particle physics
Description: We show that the flow from the ultraviolet to the infrared sector of any high-dimensional nonlinear field theory approaches chaotic dynamics in a universal way. This result stems from for the dissipative effect of non-vanishing perturbations and implies that the infrared attractor of effective field theories replicates the geometry of multifractal sets. In particular, the Standard Model (SM) Lagrangian is characterized by a dominant generalized dimension D = 2, while the same dimension of the Einstein-Hilbert Lagrangian turns out to be D = 4. On the one hand, this finding disfavors any field-theoretic unification of SM and General Relativity (GR). On the other, it hints that the continuous spectrum of dimensions lying between 2 and 4 may naturally account for the existence of non-baryonic Dark Matter.
The abstract of this article will be published in the January 2017 issue of "Intellectual Archive Bulletin", ISSN 1929-1329.
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On the Multifractal Description of Lagrangian Field Theory -v2-.pdf