Geometric Particle Creation: From Bosons to Neutrinos via Berezin Quantization on the Noncommutative Torus

We present a unified geometric theory of particle creation based on the Berezin quantization of the noncommutative torus T 2 θ emerging from the axial vortex solution in noncommutative spectral geometry. Building on the identification of the bilinear functional T (I) µν (a, b) as the Berezin operator kernel for gauge field strengths, we show that all particle creation processes—bosonic and fermionic, charged andneutral—are described by the action of specific Berezin operators on the vacuum state.The bosonic component arises from parametric resonance of coherent core oscillations, described by the Berezin operator Bω2 k(t) for the time-dependent mode frequency. The fermionic component, including both charged leptons and neutrinos, originates from spectral flow in the SU(2)L and SU(3)C sectors, encoded in the Berezin operator B ˙Q (I) CS for the Chern-Simons number rate.We provide a comprehensive analysis of **neutrino creation**, showing that neutrinos are born from the same zero modes on the torus T 2 as other fermions, but with distinct projections in the gauge sector. Four distinct channels are identified and described in the Berezin operator language:1. Direct creation from spectral flow in SU(2)L: B ˙Q (L) CS generates lepton doublets (νL, eL).2. Creation via heavy right-handed neutrinos: BYν and BMR produce νR which decay to light neutrinos.3. Secondary creation from pion decay: Bπ → BµBνµ in hadronic cascades.4. Creation via inverse beta decay in strong magnetic fields: BHint with symbol g2B2 c/m2 W.The unified Berezin operator formalism reveals that all creation processes are different projections of a single mathematical structure—the Berezin quantization map from classical symbols (fields on the torus) to quantum operators acting onthe Hilbert space of zero modes. This provides a rigorous foundation for the two-component jet model, explaining the evolution from neutrino-dominated early phases to photon-dominated late phases, and yields testable predictions for neutrino fluxes, correlations with circular polarization, and multimessenger signatures.