The Translation Invariant Massive Nelson Model: III. Asymptotic Completeness Below the Two-Boson Threshold
The Translation Invariant Massive Nelson Model: III. Asymptotic Completeness Below the Two-Boson Threshold
复制标题
平移不变大规模尼尔森模型：III。
DOI：
10.1007/s00023-014-0384-7
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
J. S. Møller
中科院分区：
文献类型：
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作者：
W. Dybalski;J. S. Møller
我们证明了一类描述单个量子粒子(电子)与质量标量场(玻色子)线性耦合的平移不变模型的二体散射的渐近完备性。我们的证明是基于最近为这些模型建立的Mourre估计。与以往的方法不同，它不需要截断数，不需要限制粒子-场的耦合强度，也不需要限制总动量的大小。然而，能量受到双玻色子阈值的限制，只允许一个修饰的电子和一个渐近玻色子的散射。我们考虑的模型包括UV截止Nelson模型和极化子模型。虽然这篇论文是一个更大的调查的一部分，但演示文稿是独立的。
We show asymptotic completeness of two-body scattering for a class of translation invariant models describing a single quantum particle (the electron) linearly coupled to a massive scalar field (bosons). Our proof is based on a recently established Mourre estimate for these models. In contrast to previous approaches, it requires no number cutoff, no restriction on the particle–field coupling strength, and no restriction on the magnitude of total momentum. Energy, however, is restricted by the two-boson threshold, admitting only scattering of a dressed electron and a single asymptotic boson. The class of models we consider includes the UV-cutoff Nelson and polaron models. Although this paper is a part of a larger investigation, the presentation is self-contained.