Rigorous Constructive Framework for a Mass Gap in Elastic Quantum Models (Part I: Flat DEM/QEM)
Year: 2025
Type: article
Abstract: We present a rigorous constructive framework for demonstrating the existence of a mass gap in Elastic Quantum Models (EQM), formulated on flat spacetime. The model couples four–dimensional Yang–Mills fields with a quantum–elastic scalar sector that ensures rigidity. By verifying the Osterwalder–Schrader axioms, we reconstruct a Hilbert space with a positive self–adjoint Hamiltonian. Uniform exponential clustering of gauge–invariant correlators implies a spectral gap: Spec(H)={0}∪[mgap,∞),mgap>0.\mathrm{Spec}(H) = \{0\} \cup [m_{\rm gap}, \infty), \quad m_{\rm gap} > 0.Spec(H)={0}∪[mgap,∞),mgap>0. The analysis is performed with lattice regularization, reflection positivity, cluster expansion, and renormalization group arguments, leading to non–trivial dynamics beyond free field theory. This work establishes a mathematically controlled proof of a mass gap in EQM, providing a new constructive approach linked to Yang–Mills theories and related to the Millennium Prize Problem.
Author: Quiroz Robles, Edgar Marcelo
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7084615875
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