On the resolvent of $H+A^{*}+A$
| Autor: | Posilicano, Andrea |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Math Phys Anal Geom 27, 11 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11040-024-09481-0 |
| Popis: | 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. Comment: revised version, denseness hypothesis of ran(A) removed |
| Databáze: | arXiv |
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