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The Stability of Matter: From Atoms to Stars

Selecta of Elliott H. Lieb

  • Book
  • © 2005

Overview

Authors:
  1. Elliott H. Lieb

    1. Departments of Mathematics and Physics Jadwin Hall, Princeton University, Princeton, USA

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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

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Table of contents (54 chapters)

  1. Front Matter

    Pages I-XV
    Download chapter PDF

  2. Introduction

    Pages 1-8

  3. Review

    1. The Stability of Matter: From Atoms to Stars

      • Elliott H. Lieb
      Pages 11-59

  4. Exact Results on Atoms

    1. Lower bound to the energy of complex atoms

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

    2. Improved Lower Bound on the Indirect Coulomb Energy

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

    3. Letter to the Editor

      • Elliott H Lieb
      Pages 79-82

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

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

    5. Atomic and Molecular Negative Ions

      • Elliott H. Lieb
      Pages 87-89

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

      • Elliott H. Lieb
      Pages 91-101

    7. Approximate Neutrality of Large-Z Ions

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

    8. Universal nature of van der Waals forces for Coulomb Systems

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

    9. Electron density near the nucleus of a large atom

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

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

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

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

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

    12. Ground states of large quantum dots in magnetic fields

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

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.

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)

Authors, Editors and Affiliations

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

    Walter Thirring

  • Departments of Mathematics and Physics Jadwin Hall, Princeton University, Princeton, USA

    Elliott H. Lieb

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