Збережено в:
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| Формат: | Recurso digital |
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| Опубліковано: |
Zenodo
2026
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| Онлайн доступ: | https://doi.org/10.5281/zenodo.20392239 |
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Зміст:
- <p class="MsoNormal"><span>We develop an extended geometric and operator-theoretic framework for the spectral analysis of Einstein–Yang–Mills Hamiltonians on compact Riemannian manifolds. Building upon coercive quadratic form methods and semibounded operator theory, the present work introduces generalized gauge-covariant Hamiltonians incorporating non-abelian curvature interactions, Ricci-induced geometric coercivity, topological gauge sectors, and generalized Weitzenböck-type identities.</span></p> <p class="MsoNormal"><span> </span><span>The analysis is formulated within a nonlinear geometric-functional framework combining Sobolev regularity, gauge-covariant elliptic operators, topological Yang–Mills structures, semibounded quadratic forms, and relatively bounded nonlinear perturbations [4–9].</span></p> <p class="MsoNormal"><span> </span><span>A generalized coercive sector is introduced in order to establish strictly positive lower spectral structures associated with admissible non-abelian gauge configurations. Using Friedrichs-type self-adjoint realizations together with generalized elliptic coercive estimates, we derive positive spectral lower bounds compatible with geometrically coupled Yang–Mills Hamiltonians.</span></p> <p class="MsoNormal"><span> </span><span>Furthermore, the present work establishes a generalized topological spectral mechanism through which gauge curvature, Ricci geometric positivity, and nontrivial topological Yang–Mills sectors generate positive spectral thresholds associated with the effective Einstein–Yang–Mills Hamiltonian.</span></p> <p class="MsoNormal"><span> </span><span>The resulting framework provides a mathematically consistent non-perturbative spectral formulation for geometrically coupled Yang–Mills systems and develops a generalized operator-theoretic mechanism through which geometric curvature and non-abelian gauge topology generate coercive lower spectral configurations.</span></p>