Quantum Mechanics, The Stability of Matter and Quantum Electrodynamics

Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and why the material world appears to be as stable as it is despite the serious −1/|x| singularity of the Coulomb potential that attracts negative electrons to positive atomic nuclei. Many problems remain, however, especially the understanding of the interaction of matter and the quantized radiation field discovered by Planck in 1900. A short review of some of the main topics is given. This paper is an extended version of a talk at the DMV Jahrestagung in Rostock, 17 November, 2003 [1]. c © 2003 by the author. This article may be reproduced, in its entirety, for noncommercial purposes. Work partially supported by U.S. National Science Foundation grant PHY 0139984A01.