The Stability of Matter in Quantum Mechanics

Description of research on the subject for researchers, and for advanced undergraduate and graduate courses in mathematical physics.

Elliott H. Lieb (Author), Robert Seiringer (Author)

9780521191180, Cambridge University Press

Hardback, published 5 November 2009

310 pages
25.4 x 18 x 2 cm, 0.7 kg

'… written at a mathematically sophisticated level and the authors are clearly masters of their subject. … subtle and fascinating definitive results obtained. … The authors invoke a classical energetic argument to inspire their approach … a comprehensive compendium of theorems and proofs in what is now a mature field that deserves to be more widely known. …heartily recommended to all physicists and mathematicians interested in the fundamental structure of matter … an up-to-date account of the mathematical theory of quantum stability.' Contemporary Physics

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.

Preface
1. Prologue
2. Introduction to elementary quantum mechanics and stability of the first kind
3. Many-particle systems and stability of the second kind
4. Lieb–Thirring and related inequalities
5. Electrostatic inequalities
6. An estimation of the indirect part of the Coulomb energy
7. Stability of non-relativistic matter
8. Stability of relativistic matter
9. Magnetic fields and the Pauli operator
10. The Dirac operator and the Brown–Ravenhall model
11. Quantized electromagnetic fields and stability of matter
12. The ionization problem, and the dependence of the energy on N and M separately
13. Gravitational stability of white dwarfs and neutron stars
14. The thermodynamic limit for Coulomb systems
References
Index.

Subject Areas: Mathematical physics [PHU], Statistical physics [PHS]