Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915133433839616 |
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| author | Hasler, David Hinrichs, Benjamin Siebert, Oliver |
| author_facet | Hasler, David Hinrichs, Benjamin Siebert, Oliver |
| contents | The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock representation, one can prove the existence of so-called dressed one-particle states. In this article, we give a simple non-perturbative proof for the existence of such one-particle states at arbitrary coupling strength and for almost all total momenta in a physically motivated momentum region. Our results hold both for the non- and the semi-relativistic Nelson model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06998 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively Hasler, David Hinrichs, Benjamin Siebert, Oliver Mathematical Physics Functional Analysis 81Q10, 46N50, 47B93, 81T15 The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock representation, one can prove the existence of so-called dressed one-particle states. In this article, we give a simple non-perturbative proof for the existence of such one-particle states at arbitrary coupling strength and for almost all total momenta in a physically motivated momentum region. Our results hold both for the non- and the semi-relativistic Nelson model. |
| title | Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively |
| topic | Mathematical Physics Functional Analysis 81Q10, 46N50, 47B93, 81T15 |
| url | https://arxiv.org/abs/2302.06998 |