A universal concept of asymptotic completeness in non-relativistic QED

渐近完备性是散射理论的核心概念之一，它要求给定系统的所有物理状态都可以用粒子来解释。虽然这一性质在量子力学中得到了很好的理解，但它在量子场论中的地位，无论是相对论的还是非相对论的，都不太清楚。在量子电动力学中，由于理论的复杂红外结构，甚至普遍接受的这一概念的表述也是缺失的。这个项目是一个更大的企业的一部分，旨在制定量子电动力学中的渐近完备性的普遍概念。这一概念应该是有意义的，在每一个标准的方法来处理这个问题，例如非相对论，代数和微扰的方法。本研究的目的是找到一个渐近完备性的概念适用于非相对论量子电动力学模型，无论其红外结构。这个概念应该与在代数量子场论框架内发展起来的对粒子方面的定性理解相一致。

Asymptotic completeness, which is one of the central concepts in scattering theory, requires that all the physical states of a given system have an interpretation in terms of particles. While this property is well understood in quantum mechanics, its status in quantum field theory, both relativistic and non-relativistic, is much less clear. In quantum electrodynamics even a generally accepted formulation of this concept is missing to date due to a complicated infrared structure of the theory.This project is a part of a larger enterprise aiming at a formulation of a universal concept of asymptotic completeness in quantum electrodynamics. This concept should be meaningful in each of the standard approaches to the subject, as forexample the non-relativistic, algebraic and perturbative approach. The present research objective is to find a notion of asymptotic completeness applicable to models of non-relativistic quantum electrodynamics, irrespectively of their infrared structure. This notion should be consistent with the qualitative understanding of particle aspects developed in the framework of algebraic quantum field theory.