Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
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量子场论中的渐近完备性：仅限于真空和单粒子扇区的平移不变纳尔逊型模型
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发表时间：
2011
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通讯作者：
M. G. Rasmussen
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作者：
C. Gérard;J. S. Møller;M. G. Rasmussen
本文研究了一大类平移不变模型的含时散射理论，包括限于真空和单粒子扇区的纳尔逊模型和极化子模型。我们制定并证明这些模型的渐近完备性。平移不变性意味着所考虑的哈密顿量相对于总动量是纤维化的。在渐近完备性的道路上，我们确定了纤维哈密顿量的谱结构，建立了一个近似估计，并推导出几何渐近完备性声明作为中间步骤。
Time-dependent scattering theory for a large class of translation invariant models, including the Nelson and Polaron models, restricted to the vacuum and one-particle sectors is studied. We formulate and prove asymptotic completeness for these models. The translation invariance imply that the Hamiltonians considered are fibered with respect to the total momentum. On the way to asymptotic completeness we determine the spectral structure of the fiber Hamiltonians, establish a Mourre estimate and derive a geometric asymptotic completeness statement as an intermediate step.