发表机构
Università dell’Insubria; Università di Milano Bicocca（因苏布里亚大学; 米兰比可卡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造并分析重整化三维有质量Lee模型的谱，通过抽象构造定义哈密顿量，利用扇区化方法证明HVZ型公式，并给出亚阈值谱缺失及束缚态存在的条件。
AI 中文摘要
我们构造并分析了一个重整化的三维有质量Lee模型；其重整化哈密顿量通过一个抽象构造内在定义，该构造明确给出了算子定义域、作用以及一个Kre\u0131n型预解公式。总激发数守恒将完整哈密顿量的谱分析简化为对一个显式算子束的谱轮廓进行扇区化研究，该算子束扮演算子值Weyl函数的角色。我们在由较低激发扇区生成的扇区中构造了本质谱分量，并获得了包含在预期的扇区化HVZ型公式中的包含关系；完整公式在前两个扇区中得到证明，并且在显式条件下在所有扇区中得到证明。在自由或单激发阈值以下，每个较高扇区中的点谱由一个有界自伴非负Birman-Schwinger算子描述。在每个至少有两个激发的扇区中，当重整化间隙不小于玻色子质量时，我们证明了任意耦合下亚阈值谱的缺失，并且当间隙较小时，在显式弱耦合条件下也证明了该缺失。在后一种情况下，我们还推导了双激发扇区中存在简单束缚态的充分条件。
英文摘要
We construct and analyze a renormalized three-dimensional massive Lee model; its renormalized Hamiltonian is defined intrinsically through an abstract construction which explicitly provides the operator domain, action and a Kre\uın-like resolvent formula. Conservation of the total excitation number reduces the spectral analysis of the full Hamiltonian to a sector-wise study of the spectral profile of an explicit operator pencil, playing the role of an operator-valued Weyl function. We construct essential spectrum components in a sector generated by lower excitation sectors and obtain the inclusion in the expected sector-wise HVZ type formula; the full formula is proved in the first two sectors and, under explicit conditions, in every sector. Below the free or one-excitation threshold, the point spectrum in every higher sector is described by a bounded self-adjoint nonnegative Birman--Schwinger operator. In every sector with at least two excitations we prove absence of sub-threshold spectrum for arbitrary coupling when the renormalized gap is not smaller than the boson mass, and under an explicit weak-coupling condition when it is smaller. In the latter case we also derive a sufficient condition for the existence of a simple bound state in the two-excitation sector.
Comments50 pages. Comments are welcome
