Authors: Ervin Goldfain
Quantum Field Theory (QFT) lies at the foundation of the Standard Model for particle physics (SM) and is built in compliance with a number of postulates called consistency conditions. The remarkable success of SM can be traced back to a unitary, local, renormalizable, gauge invariant and anomaly-free formulation of QFT. Experimental observations of recent years suggest that developing the theory beyond SM may require a careful revision of conceptual foundations of QFT. As it is known, QFT describes interaction of stable or quasi-stable fields whose evolution is deterministic and time-reversible. By contrast, behavior of strongly coupled fields or dynamics in the Terascale sector is prone to become unstable and chaotic. Nonrenormalizable interactions are likely to proliferate and prevent full cancellation of ultraviolet divergences. A specific signature of this transient regime is the onset of long-range dynamic correlations in space-time, the emergence of strange attractors in phase space and transition from smooth to fractal topology. Our focus here is the impact of fractal topology on physics unfolding above the electroweak scale. Arguments are given for perturbative renormalization of field theory on fractal space-time, breaking of discrete symmetries, hierarchical generation of particle masses and couplings as well as the potential for highly unusual phases of matter which are ultra-weakly coupled to SM. A surprising implication of this approach is that classical gravity emerges as a dual description of field theory on fractal space-time.
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