Structural Mass Emergence Theorem (SMET): A Classificatory Framework for Non-Perturbative Mass Generation in Quantum Field Theory

This thesis formulates and develops the Structural Mass Emergence Theorem (SMET), a rigorous mathematical framework for classifying the appearance of massive states in quantum field theory through localized, finite-energy stationary solutions. The work establishes necessary and sufficient conditions under which a theory without fundamental mass parameters generates a massive spectrum, unifying mechanisms such as the Skyrme model and dynamic mass generation in QCD. Numerical and analytical evidence for nontopological realizations is presented, particularly in the Dynamic Alignment Gauge Model (DAGM), and quantum stability is analyzed via the Functional Renormalization Group (FRG). Phenomenological implications include testable predictions at colliders, a deep connection with the mass gap problem in pure Yang–Mills, and possible cosmological applications such as nonthermal dark matter candidates.