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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.10496 |
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| _version_ | 1866913039120334848 |
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| author | Alvarez, Benjamin Møller, Jacob Schach |
| author_facet | Alvarez, Benjamin Møller, Jacob Schach |
| contents | We consider a class of toy models describing a fermion field coupled with a boson field. The model can be viewed as a Yukawa model but with scalar fermions. As in our first paper, the interaction kernels are assumed bounded in the fermionic momentum variable and decaying like $|q|^{-p}$ for large boson momenta $q$. With no restrictions on the coupling strength, we prove norm resolvent convergence to an ultraviolet renormalized Hamiltonian, when the ultraviolet cutoff is removed. We do this by subtracting a sufficiently large, but finite, number of recursively defined self-energy counter-terms, which may be interpreted as arising from a perturbation expansion of the ground state energy. The renormalization procedure requires a spatial cutoff and works in three dimensions provided $p>\frac12$, which is as close as one may expect to the physically natural exponent $p = \frac12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10496 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ultraviolet Renormalisation of a Quantum Field Toy Model II Alvarez, Benjamin Møller, Jacob Schach Mathematical Physics We consider a class of toy models describing a fermion field coupled with a boson field. The model can be viewed as a Yukawa model but with scalar fermions. As in our first paper, the interaction kernels are assumed bounded in the fermionic momentum variable and decaying like $|q|^{-p}$ for large boson momenta $q$. With no restrictions on the coupling strength, we prove norm resolvent convergence to an ultraviolet renormalized Hamiltonian, when the ultraviolet cutoff is removed. We do this by subtracting a sufficiently large, but finite, number of recursively defined self-energy counter-terms, which may be interpreted as arising from a perturbation expansion of the ground state energy. The renormalization procedure requires a spatial cutoff and works in three dimensions provided $p>\frac12$, which is as close as one may expect to the physically natural exponent $p = \frac12$. |
| title | Ultraviolet Renormalisation of a Quantum Field Toy Model II |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2312.10496 |