Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

在非相对论量子力学物质与量子化辐射场相互作用的标准模型中，发展了一种方法，表明在可能高度激发的束缚态中制备的孤立原子或分子是不稳定的，并最终通过发射光子而弛豫到其基态。同样，自由带电粒子的激发态也不稳定。结果表明，未被电子束缚的光子以球状逃逸，而粒子弛豫到能量最低的状态，然后是软光子云(装饰单电子状态)，在软光子云中，它根据约化的动力学进行传播。在原子的情况下，关键问题是证明不会出现红外问题。对于自由带电粒子来说，红外问题确实发生了，人们必须处理CCR的不等价表示。-证明要求对哈密顿算符的谱性质有良好的控制，此外，还要求系统的瑞利散射和康普顿散射的渐近完备性。这些前提条件是由类似于$N粒子薛定谔算符光谱和散射理论中的方法和技巧的方法和技术所建立的，如Mourre理论、传播估计、合适的传播可观测量的构造等。此外，本研究还采用了构造性量子场论(软光子界、罗森估计、重整化群分析)的思想和方法，对原子的辐射衰变、光效应和康普顿散射等物理现象有了严格的数学理解。这些现象是许多技术设备的核心，并决定了我们对世界的视觉印象。此外，辐射衰变现象(或基态的驰豫)和类似的正温度回复平衡现象在试图理解开放系统量子理论中的耗散、不可逆行为时起着关键作用。发展的数学方法同样适用于其他物理系统，如晶体中的粒子与量子化的晶格振动(声子)相互作用，目前已被应用于研究物质在正温度下与辐射相互作用的回归平衡。

Within the standard model of non-relativistic quantum mechanical matter interacting with the quantized radiation field methods are developed to show that an isolated atom or molecule prepared in a, possibly highly exited, bound state is unstable and eventually relaxes to its ground state by emitting photons. Similarly, the exited states of a free charged particle are not stable. It is shown that photons which are not bound to the electron escape ballisticly while the particle relaxes to a state of minimal energy followed by a cloud of soft photons (dressed one-electron state) in which it propagates according to a reduced dynamics. The key problem in the case of an atom is to show that no infrared problem occurs. For a free charged particle an infrared problem does occure and one has to deal with nonequivalent representations of the CCR. - The proofs require as an ingredient good control over the spectral properties of the Hamilton operator and, in addition, asymptotic completeness of Rayleigh scattering and Compton scattering of the respective system. These prerequisites are established by methods and techniques inspired by similar methods and techniques in the spectral and scattering theory of $N$-particle Schr\"odinger operators, such as Mourre theory, propagationestimates, the construction of suitable propagation observables and others. In addition ideas and methods from constructivequantum field theory (soft photon bounds, Rosen estimates, renormalization group analysis) are employed.This research leads to a mathematically rigorous understanding of physical phenomena such as the radiative decay of atoms, the photo effect, and Compton scattering. These are phenomena which are at the heart of many technical devices and which determine our visual impression of the world. Furthermore the phenomenon of radiative decay (or the relaxation to the ground state) and the similar phenomenon of return to equilibrium at positive temperature play key roles in attempts to understand dissipative, irreversible behavior in the quantum theory of open systems. The mathematical methods which are developed apply equally to other physical systems such a particle in a crystal interacting with quantized lattice vibrations (phonons), and find currently application in the study of return to equilibrium of matter interacting with radiation at positive temperature.