Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.13830 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914939118026752 |
|---|---|
| author | Posilicano, Andrea |
| author_facet | Posilicano, Andrea |
| contents | We present a much shorter and streamlined proof of an improved version of the results previously given in [A. Posilicano: On the Self-Adjointness of $H+A^{*}+A$, Math. Phys. Anal. Geom. (2020)] concerning the self-adjoint realizations of formal QFT-like Hamiltonians of the kind $H+A^{*}+A$, where $H$ and $A$ play the role of the free field Hamiltonian and of the annihilation operator respectively. We give explicit representations of the resolvent and of the self-adjointness domain; the consequent Krein-type resolvent formula leads to a characterization of these self-adjoint realizations as limit (with respect to convergence in norm resolvent sense) of cutoff Hamiltonians of the kind $H+A^{*}_{n}+A_{n}-E_{n}$, the bounded operator $E_{n}$ playing the role of a renormalizing counter term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13830 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the resolvent of $H+A^{*}+A$ Posilicano, Andrea Mathematical Physics Functional Analysis We present a much shorter and streamlined proof of an improved version of the results previously given in [A. Posilicano: On the Self-Adjointness of $H+A^{*}+A$, Math. Phys. Anal. Geom. (2020)] concerning the self-adjoint realizations of formal QFT-like Hamiltonians of the kind $H+A^{*}+A$, where $H$ and $A$ play the role of the free field Hamiltonian and of the annihilation operator respectively. We give explicit representations of the resolvent and of the self-adjointness domain; the consequent Krein-type resolvent formula leads to a characterization of these self-adjoint realizations as limit (with respect to convergence in norm resolvent sense) of cutoff Hamiltonians of the kind $H+A^{*}_{n}+A_{n}-E_{n}$, the bounded operator $E_{n}$ playing the role of a renormalizing counter term. |
| title | On the resolvent of $H+A^{*}+A$ |
| topic | Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2307.13830 |