The Stability of Matter in Quantum Mechanics

by Elliott H. Lieb, Robert Seiringer

Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics.

310 pages, Hardcover

First published November 1, 2009

Reviews

[Eric Bittner · Rating 5 out of 5]

Elliot Lieb is one of my scientific heroes and this book lives up to its reputation. Why do we have stable matter? What is the fundamental interaction that keeps my fingers from passing through this keyboard. You may think it's electron-electron (Coulomb) repulsion, but you'd be wrong. It's electron-electron exchange/correlation that arises from a fundamental symmetry for all spin 1/2 fermions. This is a MUST read for any serious student of theoretical physics.

[HikBook]

8.4 A simple kinetic energy bound
fourier(exp(-t |xi|s) for 0<=s<=2, is positive.
[150, example 2 in section XIII.12]
The function exp(-tsqrt(|p|^2+m^2) is also positive definite.

[150] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1–4,
Academic Press (1978). {pages 8, 18, 83, 146, 183, 209, 212, 223, 252.}