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Book Review

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Book Information:

Author: Elliott H. Lieb and Robert Seiringer
Title: The stability of matter in quantum mechanics
Additional book information: Cambridge University Press, Cambridge, 2010, xv+293 pp., ISBN 978-0-521-19118-0

References [Enhancements On Off] (What's this?)

  • 1. Baxter, John R., Inequalities for potentials of particle systems, Illinois J. Math. 24, 645-652 (1980). MR 586803 (82j:81065)
  • 2. Chandrasekhar, Subramanyan, The density of white dwarfstars, Phil. Mag. 11, 592-596 (1931).
  • 3. Dyson, Freeman J., Ground state energy of a finite system of charged particles, Jour. Math. Phys. 8, 1538-1545 (1967). MR 2408895 (2010c:81279)
  • 4. Dyson, Freeman J. and Lenard, Andrew, Stability of matter. I and II, Jour. Math. Phys. 8, 423-434, (1967); ibid. Jour. Math. Phys. 9, 698-711 (1968). MR 2408896 (2010e:81266)
  • 5. Fisher, Michael and Ruelle, David, The stability of many-particle systems, Jour. Math. Phys. 7, 260-270 (1966). MR 0197133 (33:5315)
  • 6. Lieb, Elliott H., The Stability of Matter, Rev.Mod. Phys., 48, 553-569, (1976). MR 0456083 (56:14314)
  • 7. Lieb, Elliott H. and Lebowitz, Joel L., The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei. Advances in Math. 9, 316-398 (1972). MR 0339751 (49:4508)
  • 8. Lieb, Elliott H. and Thirring, Walter E., Bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett. 35, 687-689 (1975).
  • 9. Lieb, Elliott H. and Thirring, Walter E., Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities, in Studies in Mathematical Physics, E. Lieb, B. Simon, A. Wightman, eds., Princeton University Press, 269-303 (1976).
  • 10. Lieb, Elliott H. and Thirring, Walter E., Gravitational Collapse in Quantum Mechanics with Relativistic Kinetic Energy, Annals of Phys. (N.Y.) 155, 494-512 (1984). MR 753345 (86g:81037)
  • 11. Lieb, Elliott H. and Yau, Horng-Tzer, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Commun. Math. Phys. 112, 147-174 (1987). MR 904142 (89b:82014)
  • 12. Lieb, Elliott H. and Yau, Horng-Tzer, The stability and instability of relativistic matter, Commun. Math. Phys. 118, 177-213 (1988). MR 956165 (90c:81251)
  • 13. Onsager, Lars, Electrostatic interaction of molecules, Jour. Phys. Chem. 43, 189-196 (1939).
  • 14. Rumin, Michel, Spectral density and Sobolev inequalities for pure and mixed states. Geom. Funct. Anal. 20 (2010). MR 2720233 (2011m:31014)
  • 15. Rumin, Michel, Balanced distribution-energy inequalities and related entropy bounds, Duke Math Journal, to appear.
  • 16. Simon, Barry, Functional Integration and Quantum Hhysics. Second edition. AMS Chelsea Publishing, Providence, RI, 2005. MR 2105995 (2005f:81003)
  • 17. Thirring, Walter, Quantum Mathematical Physics. Atoms, Molecules and Large Systems. Second edition. Springer-Verlag, Berlin, 2002. MR 2133871 (2006b:81368)

Review Information:

Reviewer: Jan Philip Solovej
Affiliation: University of Copenhagen
Email: solovej@math.ku.dk
Journal: Bull. Amer. Math. Soc. 50 (2013), 169-174
MSC (2010): Primary 81V45, 81V55, 81V70, 81C05, 81Q20, 81V17, 82A15, 35J10, 35P05, 35A23, 31B05
DOI: https://doi.org/10.1090/S0273-0979-2011-01366-0
Published electronically: December 12, 2011
Review copyright: © Copyright 2011 American Mathematical Society
American Mathematical Society