Ervin Goldfain

We have recently conjectured that the flow from the ultraviolet (UV) to the infrared (IR) sector of any multivariable field theory approaches chaotic dynamics in a universal way. A key assumption of this conjecture is that the flow evolves in far-from-equilibrium conditions and it implies that the end-point attractor of effective field theories replicates the geometry of multifractal sets. Our conclusions are further reinforced here in the framework of nonlinear dynamical systems and bifurcation theory. In particular, it is found that steady-state perturbations near the IR attractor induce formation of Dark Matter structures while oscillatory perturbations lead to the field content of the Standard Model.

We have recently conjectured that the flow from the ultraviolet (UV) to the infrared (IR) sector of any multivariable field theory approaches chaotic dynamics in a universal way. A key assumption of this conjecture is that the flow evolves in far-from-equilibrium conditions and it implies that the end-point attractor of effective field theories replicates the geometry of multifractal sets. Our conclusions are further reinforced here in the framework of nonlinear dynamical systems and bifurcation theory. In particular, it is found that steady-state perturbations near the IR attractor induce formation of Dark Matter structures while oscillatory perturbations lead to the field content of the Standard Model.

We have recently conjectured that the flow from the ultraviolet (UV) to the infrared (IR) sector of any multivariable field theory approaches chaotic dynamics in a universal way. A key assumption of this conjecture is that the flow evolves in far-from-equilibrium conditions and it implies that the end-point attractor of effective field theories replicates the geometry of multifractal sets. Our conclusions are further reinforced here in the framework of nonlinear dynamical systems and bifurcation theory. In particular, it is found that steady-state perturbations near the IR attractor induce formation of Dark Matter structures while oscillatory perturbations lead to the field content of the Standard Model.

We show that relativistic invariance is encoded in the multifractal structure of the Standard Model near the electroweak scale. The approximate scale invariance of this structure accounts for the flavor hierarchy and chiral symmetry breaking in the electroweak sector. Surprisingly, it also accounts for breaking of conformal symmetry in General Relativity and the emergence of a non-vanishing cosmological constant.

We show that the flow from the ultraviolet to the infrared sector of any multidimensional nonlinear field theory approaches chaotic dynamics in a universal way. This result stems from several independent routes to aperiodic behavior and implies that the infrared attractor of effective field theories is likely to replicate the geometry of multifractal sets. In particular, we find that the Einstein-Hilbert Lagrangian is characterized by a single generalized dimension (D = 2 ), while the Standard Model (SM) Lagrangian is defined by a triplet of generalized dimensions (D = 2, 3 and  4 ). On the one hand, this finding disfavors any naïve field-theoretic unification of SM and General Relativity (GR). On the other, it hints that the continuous spectrum of generalized dimensions lying between 2  and 4 may naturally account for the existence of non-baryonic Dark Matter.

We develop field theoretic arguments for the unification of relativistic gravity with Standard Model interactions acting on high-energy scales. The work is founded on two premises: i) the fundamental principle of local gauge invariance and ii) local scaling invariance applied to space-time and fermion fields undergoing critical behavior near the Cohen-Kaplan threshold. We focus on the transition boundary between the classical and non-classical regime, the latter being characterized by generalized scaling laws with continuously varying exponents. It is shown that both gravitational field and Standard Model interactions emerge from local changes in the nontrivial geometry of space-time near this transition boundary.

A novel concept on the construction of high-resolution objectives is outlined. Although similar to binary optics technology, this approach brings additional degrees of freedom to the optical design as far as achieving a finer balance of phase curvature via refractive properties and relative thickness of the multilayer stack. The differential coating objective can be used in conjunction with diffractive surfaces to optimize the transmission efficiency and control the secondary spectrum correction. The basic equations describing the monochromatic and three- color achromat predesign are presented.

The gauge hierarchy problem in particle physics refers to the large numerical disparity between the value of the Planck mass and the mass scale of the electroweak interaction. Explaining the hierarchy paradox has been attempted so far in quantum field models based on supersymmetry or higher dimensional space-time with a large number of extra dimensions (brane theories). Despite several years of experimental search, there is currently no validation for either one of these models. We approach the hierarchy paradox using the methodology of fractal operators in four-dimensional space-time. It is found that departure from the inverse-square gravity in the high-energy regime emerges naturally from the fractional Helmholtz equation and offers a simple resolution to the problem. Our work makes an explicit connection between the hierarchy problem and Cantorian geometry of space-time on energy scales comparable to the Planck mass.

Both classical and quantum electrodynamics assume that random fluctuations are absent from the steady state evolution of the underlying physical system.This work goes beyond this approximation and accounts for the continuous exposure to stochastic fluctuations.It was recently shown that the asymptotic limit of quantum field dynamics, dominated by large and persistent perturbations,may be described as an anomalous diffusion process.We use fractional calculus as an appropiate tool to handle this highly nontrivial regime.It is shown that the fine structure constant can be recovered from the fractional evolution equation of the density matrix under standard normalization conditions.

We report a derivation of lepton and vector boson masses using a bifurcation analysis of the Higgs-free field lagrangian. The equations of motion describing the classical Yang-Mills-Dirac massless theory are investigated in a planar differential form. The analysis of the resulting bifurcation set indicates that: 1) the gauge vacuum coincides with either one of the two vector bosons (W,Z), 2) the boson selfcoupling obeys the Feigenbaum scaling law. Placing the control parameters on the bifurcation set retrieves the low- energy pattern of lepton masses. Predictions are shown to be consistent with experimental data.