Complex Dynamics and the High-energy Regime of Quantum Field Theory

The standard model embodies our current knowledge of elementary particle physics and represents a welltested framework for the study of non-gravitational phenomena at low energies. It is built on the foundations of relativistic quantum field theory (QFT), which provides the correct description of electroweak and strong interactions involving leptons and quarks. It is generally believed that, extending the validity of QFT to energies on or beyond the TeV range must include the unavoidable signature of vacuum fluctuations and strong-field gravity. We argue that an effective approach to the high-energy regime of QFT demands the tools of complex dynamics and fractal operators. The unexpected consequences of using fractal operators to model complexity beyond the current range of QFT are outlined and discussed.