Book Review
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MathSciNet review:
2995000
Full text of 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
J. R. Baxter, Inequalities for potentials of particle systems, Illinois J. Math. 24 (1980), no. 4, 645–652. MR 586803
Chandrasekhar, Subramanyan, The density of white dwarfstars, Phil. Mag. 11, 592–596 (1931).
Freeman J. Dyson, Ground-state energy of a finite system of charged particles, J. Math. Phys. 8 (1967), no. 8, 1538–1545. MR 2408895, DOI 10.1063/1.1705389
Freeman J. Dyson and A. Lenard, Stability of matter. I, J. Math. Phys. 8 (1967), no. 3, 423–434. MR 2408896, DOI 10.1063/1.1705209
Michael E. Fisher and David Ruelle, The stability of many-particle systems, J. Mathematical Phys. 7 (1966), 260–270. MR 197133, DOI 10.1063/1.1704928
Elliott H. Lieb, The stability of matter, Rev. Modern Phys. 48 (1976), no. 4, 553–569. MR 0456083, DOI 10.1103/RevModPhys.48.553
Elliott H. Lieb and Joel L. Lebowitz, The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei, Advances in Math. 9 (1972), 316–398. MR 339751, DOI 10.1016/0001-8708(72)90023-0
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).
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).
Elliott H. Lieb and Walter E. Thirring, Gravitational collapse in quantum mechanics with relativistic kinetic energy, Ann. Physics 155 (1984), no. 2, 494–512. MR 753345, DOI 10.1016/0003-4916(84)90010-1
Elliott H. Lieb and Horng-Tzer Yau, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Comm. Math. Phys. 112 (1987), no. 1, 147–174. MR 904142
Elliott H. Lieb and Horng-Tzer Yau, The stability and instability of relativistic matter, Comm. Math. Phys. 118 (1988), no. 2, 177–213. MR 956165
Onsager, Lars, Electrostatic interaction of molecules, Jour. Phys. Chem. 43, 189–196 (1939).
Michel Rumin, Spectral density and Sobolev inequalities for pure and mixed states, Geom. Funct. Anal. 20 (2010), no. 3, 817–844. MR 2720233, DOI 10.1007/s00039-010-0075-6
Rumin, Michel, Balanced distribution-energy inequalities and related entropy bounds, Duke Math Journal, to appear.
Barry Simon, Functional integration and quantum physics, 2nd ed., AMS Chelsea Publishing, Providence, RI, 2005. MR 2105995, DOI 10.1090/chel/351
Walter Thirring, Quantum mathematical physics, 2nd ed., Springer-Verlag, Berlin, 2002. Atoms, molecules and large systems; Translated from the 1979 and 1980 German originals by Evans M. Harrell II. MR 2133871, DOI 10.1007/978-3-662-05008-8
References
- Baxter, John R., Inequalities for potentials of particle systems, Illinois J. Math. 24, 645–652 (1980). MR 586803 (82j:81065)
- Chandrasekhar, Subramanyan, The density of white dwarfstars, Phil. Mag. 11, 592–596 (1931).
- Dyson, Freeman J., Ground state energy of a finite system of charged particles, Jour. Math. Phys. 8, 1538–1545 (1967). MR 2408895 (2010c:81279)
- 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)
- Fisher, Michael and Ruelle, David, The stability of many-particle systems, Jour. Math. Phys. 7, 260–270 (1966). MR 0197133 (33:5315)
- Lieb, Elliott H., The Stability of Matter, Rev. Mod. Phys., 48, 553–569, (1976). MR 0456083 (56:14314)
- 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)
- 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).
- 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).
- 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)
- 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)
- 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)
- Onsager, Lars, Electrostatic interaction of molecules, Jour. Phys. Chem. 43, 189–196 (1939).
- Rumin, Michel, Spectral density and Sobolev inequalities for pure and mixed states. Geom. Funct. Anal. 20 (2010). MR 2720233 (2011m:31014)
- Rumin, Michel, Balanced distribution-energy inequalities and related entropy bounds, Duke Math Journal, to appear.
- Simon, Barry, Functional Integration and Quantum Hhysics. Second edition. AMS Chelsea Publishing, Providence, RI, 2005. MR 2105995 (2005f:81003)
- 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
DOI:
https://doi.org/10.1090/S0273-0979-2011-01366-0
Published electronically:
December 12, 2011
Review copyright:
© Copyright 2011
American Mathematical Society
