The Stability of Matter: From Atoms to Stars

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

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.

• Boson System
• Mathematische Methoden
• Mathematische Physik
• QED
• Thermodynamic Limit
• Thomas-Fermi Theory
• functional analysis
• quantum mechanics

 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)

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

  Walter Thirring

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