Fractional dynamics and the TeV regime of field theory

Fractional dynamics offers a reliable tool for the study of far-from equilibrium processes that display scale-invariant properties, dissipation and long-range correlations. This is particularly attractive when dealing with the complex dynamics generated in the deep ultraviolet regime of quantum field theory. We analyze a simple scalar field Lagrangian using Caputo derivatives and the approximation of low-level fractionality. Results may be extrapolated to more realistic field models and suggest a series of surprising implications regarding phenomena that are expected to emerge beyond the range of the standard model for particle physics.