Spectral Projection, Perturbative Response, and Spectral Action for Quantum Hamiltonians
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866901268478296064 |
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| author | Kim, Andrew |
| author_facet | Kim, Andrew |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19057909 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Spectral Projection, Perturbative Response, and Spectral Action for Quantum Hamiltonians Kim, Andrew Spectral theory Quantum Hamiltonians Spectral action Heat kernel asymptotics Gauge fields Resolvent operators Perturbation theory Dirac operators <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> |
| title | Spectral Projection, Perturbative Response, and Spectral Action for Quantum Hamiltonians |
| topic | Spectral theory Quantum Hamiltonians Spectral action Heat kernel asymptotics Gauge fields Resolvent operators Perturbation theory Dirac operators |
| url | https://doi.org/10.5281/zenodo.19057909 |