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The Stability of Matter: From Atoms to Stars

Selecta of Elliott H. Lieb

  • Book
  • © 2001

Overview

Editors:
  1. Walter Thirring

    1. Institut für Theoretische Physik, Universität Wien, Wien, Austria

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  • Elliott H. Lieb has been awarded the Rolf Schock Prize in Mathematics of the Swedish Academy of Sciences for 2001 for his outstanding work in mathematical physics, particularly for his contribution to the mathematical understanding of the quantum-mechanical many-body theory and for his work on exact solutions of models in statistical mechanics and quantum mechanics

  • Includes supplementary material: sn.pub/extras

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Table of contents (49 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Introduction

    1. Introduction

      • Walter Thirring
      Pages 1-8

  3. Review

    1. Front Matter

      Pages 9-9
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    2. The Stability of Matter: From Atoms to Stars

      • Elliott H. Lieb
      Pages 11-59

  4. Exact Results on Atoms

    1. Front Matter

      Pages 61-61
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    2. Lower bound to the energy of complex atoms

      • Peter Hertel, Elliot H. Lieb, Walter Thirring
      Pages 63-64

    3. Improved Lower Bound on the Indirect Coulomb Energy

      • Elliott H. Lieb, Stephen Oxford
      Pages 65-77

    4. Monotonicity of the molecular electronic energy in the nuclear coordinates

      • Elliott H. Lieb
      Pages 79-82

    5. Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle

      • Rafael Benguria, Elliott H. Lieb
      Pages 83-86

    6. Atomic and Molecular Negative Ions

      • Elliott H. Lieb
      Pages 87-89

    7. Bound on the maximum negative ionization of atoms and molecules

      • Elliott H. Lieb
      Pages 91-101

    8. Approximate Neutrality of Large-Z Ions

      • Elliott H. Lieb, Israel M. Sigal, Barry Simon, Walter Thirring
      Pages 103-112

    9. Universal nature of van der Waals forces for Coulomb systems

      • Elliott H. Lieb, Walter E. Thirring
      Pages 113-119

    10. Electron density near the nucleus of a large atom

      • Ole J. Heilmann, Elliott H. Lieb
      Pages 121-126

    11. Proof of a conjecture about atomic and molecular cores related to Scott’s correction

      • Alexei Iantchenko, Elliott H. Lieb, Heinz Siedentop
      Pages 127-145

    12. Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields

      • Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 147-169

    13. Ground states of large quantum dots in magnetic fields

      • Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 171-190

  5. General Results with Applications to Atoms

    1. Front Matter

      Pages 191-191
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    2. Kinetic Energy Bounds and Their Application to the Stability of Matter

      • Elliott H. Lieb
      Pages 193-204

    3. Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities

      • Elliott H. Lieb, Walter E. Thirring
      Pages 205-239
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About this book

The second edition of this "selecta" of my work on the stability of matter was sold out and this presented an opportunity to add some newer work on the quantum­ mechanical many-body problem. In order to do so, and still keep the volume within manageable limits, it was necessary to delete a few papers that appeared in the previous editions. This was done without sacrificing content, however, since the material contained in the deleted papers still appears, in abbreviated form, at least, in other papers reprinted here. Seetions VII and VIII are new. The former is on quantum electrodynamics (QED), to which I was led by consideration of stability of the non-relativistic many-body Coulomb problem, as contained in the first and second editions. In particular, the fragility of stability of matter with c1assical magnetic fields, which requires abound on the fine-structure constant even in the non-relativistic case (item V.4), leads to the question of stability in a theory with quantized fields. There are many unresolved problems of QED if one attempts to develop a non­ perturbative theory - as everyone knows. A non-perturbative theory is essential, however, if one is going to understand the stability of the many-body problem, which is the stability of ordinary matter. Some physicists will say that a non­ perturbative QED does not exist - and this might be true in the absence of cutoffs - but an effective theory with cutoffs of a few Mev must exist since matter exists.

Reviews

 From the reviews:

"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)

Editors and Affiliations

  • Institut für Theoretische Physik, Universität Wien, Wien, Austria

    Walter Thirring

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