The Stability of Matter: From Atoms to Stars

Selecta of Elliott H. Lieb

By: Walter Thirring (Editor), F. Dyson (Preface by), Elliott H. Lieb

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Hardcover | 29 November 2004 | Edition Number 4

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Hardcover
932 Pages

Edition Type
Revised

Dimensions(cm)
22.9 x 15.2 x 4.93

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$349.17

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This fourth edition of selecta of my work on the stability of matter contains recent work on two topics that continue to fascinate me: Quantum electrodynamics (QED) and the Bose gas. Three papers have been added to Part VII on QED. As I mentioned in the preface to the third edition, there must be a way to formulate a non-perturbative QED, presumably with an ultraviolet cutoff, that correctly describes low energy physics, i.e., ordinary matter and its interaction with the electromagnetic field. The new paper VII.5, which "quantizes" the results in V.9, shows that the elementary 'no-pair' version of relativistic QED (using the Dirac operator) is unstable when many-body effects are taken into account. Stability can be restored, however, if the Dirac operator with the field, instead of the bare Dirac operator, is used to define an electron. Thus, the notion of a "bare" electron without its self-field is physically questionable.

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"The rapid soldout of the two previous editions by itself demonstrates the high value of this book. The reader will have indeed the opportunity to gaze on the formidable mastering of functional analysis by Elliot Lieb and to discover mathematical and Physical depths in the description of, after all, familar physical phenomena. [...] The third edition contains new developments compared to previous ones, witnessing that the field is still lively. In particular there are important results concerning systems of bosons. [...] In conclusion, this book is a delight for readers interested in the stability and related properties of many-body systems. It, moreover, offers the oppertunity to admire the elegant mathematical considerations and the penetrating physical insight of a great theoretician." (Physicalia, 2002)

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The stability of matter : from atoms to stars	p. 11
Lower bound to the energy of complex atoms	p. 63
Improved lower bound on the indirect Coulomb energy	p. 65
Monotonicity of the molecular electronic energy in the nuclear coordinates	p. 79
Proof of the stability of highly negative ions in the absence of the Pauli principle	p. 83
Atomic and molecular negative ions	p. 87
Bound on the maximum negative ionization of atoms and molecules	p. 91
Approximate neutrality of large-Z ions	p. 103
Universal nature of van der Waals forces for Coulomb systems	p. 113
Electron density near the nucleus of a large atom	p. 121
Proof of a conjecture about atomic and molecular cores related to Scott's correction	p. 127
Asymptotics of natural and artificial atoms in strong magnetic fields	p. 147
Ground states of large quantum dots in magnetic fields	p. 171
Kinetic energy bounds and their application to the stability of matter	p. 193
Inequalities for the moments of the eigenvalues of the Schrodinger Hamiltonian and their relation to Sobolev inequalities	p. 205
On semi-classical bounds for eigenvalues of Schrodinger operators	p. 241
The number of bound states of one-body Schrodinger operators and the Weyl problem	p. 245
Variational principle for many-fermion systems	p. 257
Thomas-Fermi and related theories of atoms and molecules	p. 263
The Hartree-Fock theory for Coulomb systems	p. 303
There are no unfilled shells in unrestricted Hartree-Fock theory	p. 313
Many-body atomic potentials in Thomas-Fermi theory	p. 317
The positivity of the pressure in Thomas-Fermi theory	p. 329
The Thomas-Fermi-von Weizsacker theory of atoms and molecules	p. 357
Analysis of the Thomas-Fermi-von Weizsacker equation for an infinite atom without electron repulsion	p. 371
The most negative ion in the Thomas-Fermi-von Weizsacker theory of atoms and molecules	p. 383
Bound for the kinetic energy of fermions which proves the stability of matter	p. 401
Stability of coulomb systems with magnetic fields, I : the one-electron atom	p. 405
Stability of coulomb systems with magnetic fields, II : the many-electron atom and the one-electron molecule	p. 425
Stability of matter in magnetic fields	p. 437
The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics	p. 443
One-electron relativistic molecules with Coulomb interaction	p. 471
The stability and instability of relativistic matter	p. 485
Stability of relativistic matter via Thomas-Fermi theory	p. 523
Stability and instability of relativistic electrons in classical electromagnetic fields	p. 535
The stability of matter	p. 561
Existence of thermodynamics for real matter with Coulomb forces	p. 579
The thermodynamic limit for jellium	p. 583
Self energy of electrons in non-perturbative QED	p. 607
Ground-states in non-relativistic quantum electrodynamics	p. 625
Existence of atoms and moleculesin non-relativistic quantum electrodynamics	p. 665
A bound on binding energies and mass renormalization in models of quantum electrodynamics	p. 709
Stability of a model of relativistic quantum electrodynamics	p. 723
Ground state energy of the low density Bose gas	p. 755
Bosons in a trap : a rigorous derivation of the Gross-Pitaevskii energy functional	p. 759
The N[superscript 5/3] law for bosons	p. 773
The N[superscript 7/5] law for charged bosons	p. 777
Ground state energy of the one-component charged Bose gas	p. 809
Ground state energy of the two-component charged Bose gas	p. 849
Proof of Bose-Einstein condensation for dilute trapped gases	p. 899
Superfluidity in dilute trapped Bose gases	p. 903
One-dimensional bosons in three-dimensional traps	p. 909
Selecta of Elliott H. Lieb	p. 913
Publications of Elliott H. Lieb	p. 915
Table of Contents provided by Blackwell. All Rights Reserved.

The Stability of Matter: From Atoms to Stars

Selecta of Elliott H. Lieb

At a Glance

Hardcover

Industry Reviews

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