
We present a resonance-based framework in which elementary par-ticles correspond to eigenmodes of a fundamental resonance operator.Particle masses emerge as spectral eigenvalues, while interactions arisefrom nonlinear couplings of resonance fields.A bifurcation in the resonance pole structure provides a possiblemechanism for the emergence of three particle generations. Empir-ical relations such as the Koide relation for charged leptons appearnaturally within a phase-symmetric resonance spectrum.Spacetime geometry is proposed to emerge from correlation struc-tures of the resonance field.
spectral operators bifurcation theory nonlinear field theory eigenmode physics, dark matter models vacuum energy problem, resonance model resonance operator spectral particle physics resonance field theory, particle mass spectrum fermion generations particle mass hierarchy CKM mixing lepton mass relations Koide relation, beyond the Standard Model emergent spacetime emergent gravity quantum field theory extensions
spectral operators bifurcation theory nonlinear field theory eigenmode physics, dark matter models vacuum energy problem, resonance model resonance operator spectral particle physics resonance field theory, particle mass spectrum fermion generations particle mass hierarchy CKM mixing lepton mass relations Koide relation, beyond the Standard Model emergent spacetime emergent gravity quantum field theory extensions
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