Dyson expansion for form-bounded perturbations, and applications to the polaron problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914201884164096 |
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| author | Desio, Davide Seiringer, Robert |
| author_facet | Desio, Davide Seiringer, Robert |
| contents | We present an abstract Dyson expansion for perturbations that are merely relatively form-bounded, and apply it to the polaron problem. For a large class of polaron-type models, including the Fröhlich and Nelson models, we prove that the vacuum expectation value of the heat semi-group is a completely monotone function of the square of the total momentum. Consequently, the ground state energy is a concave function of the square of the momentum, a result recently proved for the Fröhlich model in \cite{polzer} using a probabilistic approach via Wiener integrals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dyson expansion for form-bounded perturbations, and applications to the polaron problem Desio, Davide Seiringer, Robert Mathematical Physics We present an abstract Dyson expansion for perturbations that are merely relatively form-bounded, and apply it to the polaron problem. For a large class of polaron-type models, including the Fröhlich and Nelson models, we prove that the vacuum expectation value of the heat semi-group is a completely monotone function of the square of the total momentum. Consequently, the ground state energy is a concave function of the square of the momentum, a result recently proved for the Fröhlich model in \cite{polzer} using a probabilistic approach via Wiener integrals. |
| title | Dyson expansion for form-bounded perturbations, and applications to the polaron problem |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2512.13443 |