Quantum fields as critical waves

This paper demonstrates a novel mechanism for the emergence of particle-like mass within the recently proposed Critical Field Theory framework. The approach is based on nonlinear self-interactions of a single Abelian gauge field and a gauge-invariant Lagrangian structure, allowing massive-like localized excitations to emerge without auxiliary scalar fields, such as the Higgs field. In particular, we show how a nonlinear critical transition from delocalized oscillatory dynamics to strongly localized field configurations can produce a massive-like dispersion relation, while conserving the energy of the underlying field. Previous applications of this framework to gravitational and cosmological phenomena, including redshift dynamics, galaxy rotation curves, and gravitational lensing, motivate the broader possibility that quantum, gravitational, and electromagnetic phenomena may share a common critical dynamical field origin. The present work provides a concrete demonstration of this possibility through the emergence of mass-like behavior from nonlinear electromagnetic field dynamics.