论文标题
关于h+a*+a的自相关性
On the self-adjointness of H+A*+A
论文作者
论文摘要
令$ h：d（h）\ subseteq {\ mathscr f} \ to {\ mathscr f} $为sexchaint，让$ a：d（h）\ to {\ mathscr f} $（扮演nihihilator操作员的角色）是$ h $ by-by-by-by-by-by-by-by-bonked。假设$ a $（以便创建操作员$ a^{*} $是$ h $的单一扰动），通过双重应用，我们建立了自我追加实现$ \ hat h $ hat hat hat hat hat hat $ h+a+a^$ a^$ a^$ a^$ a $ h）= \ {0 \} $。我们给出$ d（\ hat H）$的明确表征，并为分解差$（ - \ hat H+z）^{ - 1} - （ - H+Z）^{ - 1} $提供公式。此外，我们将$ \ hat h $的描述的问题视为一种（规范的解决）$ h+h+a+a^{*} _ {n}+a_ {n}+a_ {n}+e_ {n} $，其中$ a_ {n} \！操作员。这些结果表明，kerin的分解公式与自相关操作员的奇异扰动与量子场理论中可重新分析模型的非扰动理论之间的联系。特别是，作为一个明确的例子，我们考虑纳尔逊模型。
Let $H:D(H)\subseteq{\mathscr F}\to{\mathscr F}$ be self-adjoint and let $A:D(H)\to{\mathscr F}$ (playing the role of the annihilator operator) be $H$-bounded. Assuming some additional hypotheses on $A$ (so that the creation operator $A^{*}$ is a singular perturbation of $H$), by a twofold application of a resolvent Krein-type formula, we build self-adjoint realizations $\hat H$ of the formal Hamiltonian $H+A^{*}+A$ with $D(H)\cap D(\hat H)=\{0\}$. We give an explicit characterization of $D(\hat H)$ and provide a formula for the resolvent difference $(-\hat H+z)^{-1}-(-H+z)^{-1}$. Moreover, we consider the problem of the description of $\hat H$ as a (norm resolvent) limit of sequences of the kind $H+A^{*}_{n}+A_{n}+E_{n}$, where the $A_{n}\!$'s are regularized operators approximating $A$ and the $E_{n}$'s are suitable renormalizing bounded operators. These results show the connection between the construction of singular perturbations of self-adjoint operators by Krein's resolvent formula and nonperturbative theory of renormalizable models in Quantum Field Theory; in particular, as an explicit example, we consider the Nelson model.
