Quantum Electrodynamics of Non-relativistic Particles: the Theory of Radiation

Abstract

We conclude this book by outlining the theory of the phenomenon of emission and absorption of electromagnetic radiation by systems of non-relativistic particles such as atoms and molecules. Attempts to understand this phenomenon led, at the beginning of the twentieth century, to the birth of quantum physics. Only by treating the matter and the radiation as quantum mechanical can one give a consistent description of the phenomenon in question. Thus, our starting point should be a Schrodinger operator describing quantum particles interacting amongst themselves, and with quantum radiation. In mathematical terms, the question we address is how the bound state structure of the particle system is modified by the interaction with radiation. One expects that the ground state of the particle system survives, while the excited states turn into resonances. The real parts of the resonance eigenvalues — the resonance energies — produce the Lamb shift, first experimentally measured by Lamb and Retherford (Lamb was awarded the Nobel prize for this discovery). The imaginary parts of the resonance eigenvalues — the decay probabilities — are given by the Fermi Golden Rule (see, eg, [HuS]). This picture was established rigorously, under somewhat restrictive conditions, in [BFS1]- [BFS4], whose results we describe here. The method in these papers also provides an effective computational technique to any order in the electron charge, something the conventional perturbation theory fails to do.