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| Автор: | |
|---|---|
| Формат: | Recurso digital |
| Мова: | Англійська |
| Опубліковано: |
Zenodo
2026
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| Предмети: | |
| Онлайн доступ: | https://doi.org/10.5281/zenodo.19057909 |
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Зміст:
- <p>We present a unified operator-theoretic formulation of spectral projection, perturbative response, and spectral action for self-adjoint quantum Hamiltonians. The framework is based on Riesz projections associated with isolated ground states and introduces a trace-class interaction functional comparing spectral projectors.</p> <p>The construction is related to standard perturbation theory, resolvent identities, and determinant formulations, providing a common trace-based description of spectral response. In the presence of Dirac-type operators coupled to gauge connections, the spectral action expansion recovers curvature-dependent contributions through heat kernel asymptotics, including terms consistent with Yang–Mills functionals.</p> <p>The results are structural and organize established tools in spectral theory and mathematical physics, clarifying their role in quantum Hamiltonian systems and spectral action formulations.</p>