The Stability of Matter in Quantum Mechanics

Erscheinungsjahr 2009
ISBN: 978-0-521-19118-0
Verlag: Cambridge University Press

Buch, Englisch, 310 Seiten, Format (B × H): 179 mm x 253 mm, Gewicht: 682 g

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.

Autoren/Hrsg.

Lieb, Elliott H

Seiringer, Robert

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.

Über Autor(innen)

Seiringer, Robert
Robert Seiringer is an Assistant Professor of Physics at Princeton University. His research is centred largely on the quantum-mechanical many-body problem, and has been recognized by a Fellowship of the Sloan Foundation, by a U.S. National Science Foundation Early Career award, and by the 2009 Poincaré prize of the International Association of Mathematical Physics.

Lieb, Elliott H
Elliott H. Lieb is a Professor of Mathematics and Higgins Professor of Physics at Princeton University. He has been a leader of research in mathematical physics for many decades, and his achievements have earned him numerous prizes and awards, including the Heineman Prize in Mathematical Physics of the American Physical Society, the Max-Planck medal of the German Physical Society, the Boltzmann medal of the International Union of Pure and Applied Physics, the Schock prize in mathematics by the Swedish Academy of Sciences, the Birkhoff prize in applied mathematics of the American Mathematical Society, the Austrian Medal of Honor for Science and Art, and the Poincaré prize of the International Association of Mathematical Physics.

Elliott H. Lieb is a Professor of Mathematics and Higgins Professor of Physics at Princeton University. He has been a leader of research in mathematical physics for many decades, and his achievements have earned him numerous prizes and awards, including the Heineman Prize in Mathematical Physics of the American Physical Society, the Max-Planck medal of the German Physical Society, the Boltzmann medal of the International Union of Pure and Applied Physics, the Schock prize in mathematics by the Swedish Academy of Sciences, the Birkhoff prize in applied mathematics of the American Mathematical Society, the Austrian Medal of Honor for Science and Art, and the Poincaré prize of the International Association of Mathematical Physics.

Robert Seiringer is an Assistant Professor of Physics at Princeton University. His research is centred largely on the quantum-mechanical many-body problem, and has been recognized by a Fellowship of the Sloan Foundation, by a U.S. National Science Foundation Early Career award, and by the 2009 Poincaré prize of the International Association of Mathematical Physics.