Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915728855138304 |
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| author | Gamet, Thomas |
| author_facet | Gamet, Thomas |
| contents | We study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free part and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian via Bogoliubov transformations, thus simplifying its definition as a self-adjoint operator. Depending on the field operator's smearing, we discuss different renormalizations, either of the energy alone, or the energy and coupling constant together. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations Gamet, Thomas Mathematical Physics Spectral Theory We study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free part and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian via Bogoliubov transformations, thus simplifying its definition as a self-adjoint operator. Depending on the field operator's smearing, we discuss different renormalizations, either of the energy alone, or the energy and coupling constant together. |
| title | Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2506.08590 |