{"title":"论 H+A $$^{*}$ +A 的溶剂","authors":"Andrea Posilicano","doi":"10.1007/s11040-024-09481-0","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(H+A^{*}+A\\)</span>. <i>Math. Phys. Anal. Geom.</i> <b>23</b> (2020)] concerning the self-adjoint realizations of formal QFT-like Hamiltonians of the kind <span>\\(H+A^{*}+A\\)</span>, where <i>H</i> and <i>A</i> 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 Kreĭn-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 <span>\\(H+A^{*}_{n}+A_{n}-E_{n}\\)</span>, the bounded operator <span>\\(E_{n}\\)</span> playing the role of a renormalizing counter term. These abstract results apply to various concrete models in Quantum Field Theory.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 3","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09481-0.pdf","citationCount":"0","resultStr":"{\"title\":\"On the Resolvent of H+A\\\\(^{*}\\\\)+A\",\"authors\":\"Andrea Posilicano\",\"doi\":\"10.1007/s11040-024-09481-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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 <span>\\\\(H+A^{*}+A\\\\)</span>. <i>Math. Phys. Anal. Geom.</i> <b>23</b> (2020)] concerning the self-adjoint realizations of formal QFT-like Hamiltonians of the kind <span>\\\\(H+A^{*}+A\\\\)</span>, where <i>H</i> and <i>A</i> 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 Kreĭn-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 <span>\\\\(H+A^{*}_{n}+A_{n}-E_{n}\\\\)</span>, the bounded operator <span>\\\\(E_{n}\\\\)</span> playing the role of a renormalizing counter term. These abstract results apply to various concrete models in Quantum Field Theory.</p></div>\",\"PeriodicalId\":694,\"journal\":{\"name\":\"Mathematical Physics, Analysis and Geometry\",\"volume\":\"27 3\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11040-024-09481-0.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Physics, Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11040-024-09481-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-024-09481-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
我们对先前在 [A.Posilicano:On the Self-Adjointness of \(H+A^{*}+A\).Math.Phys.Geom.23 (2020)] 关于形式 QFT 类哈密顿的自相交实现的 \(H+A^{*}+A\),其中 H 和 A 分别扮演自由场哈密顿和湮灭算子的角色。我们给出了解析域和自相接域的显式表示;随后的克雷昂式解析式导致了这些自相接实现作为 \(H+A^{*}_{n}+A_{n}-E_{n}\)类型的截止哈密顿的极限(关于规范解析意义上的收敛)的特征,有界算子 \(E_{n}\)扮演了重正化反项的角色。这些抽象结果适用于量子场论的各种具体模型。
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.23 (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 Kreĭn-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. These abstract results apply to various concrete models in Quantum Field Theory.
期刊介绍:
MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas.
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