The stability of matter : from atoms to stars : selecta of Elliott H. Lieb

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. Front Matter....Pages I-XIII Introduction....Pages 1-8 Front Matter....Pages 9-9 The Stability of Matter: From Atoms to Stars....Pages 11-59 Front Matter....Pages 61-61 Lower bound to the energy of complex atoms....Pages 63-64 Improved Lower Bound on the Indirect Coulomb Energy....Pages 65-77 Monotonicity of the molecular electronic energy in the nuclear coordinates....Pages 79-82 Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle....Pages 83-86 Atomic and Molecular Negative Ions....Pages 87-89 Bound on the maximum negative ionization of atoms and molecules....Pages 91-101 Approximate Neutrality of Large- Z Ions....Pages 103-112 Universal nature of van der Waals forces for Coulomb systems....Pages 113-119 Electron density near the nucleus of a large atom....Pages 121-126 Proof of a conjecture about atomic and molecular cores related to Scott’s correction....Pages 127-145 Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields....Pages 147-169 Ground states of large quantum dots in magnetic fields....Pages 171-190 Front Matter....Pages 191-191 Kinetic Energy Bounds and Their Application to the Stability of Matter....Pages 193-204 Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities....Pages 205-239 On Semi-Classical Bounds for Eigenvalues of SchröDinger Operators....Pages 241-243 The Number of Bound States of One-Body Schroedinger Operators and the Weyl Problem....Pages 245-256 Variational Principle for Many-Fermion Systems....Pages 257-259 Front Matter....Pages 261-261 Thomas-fermi and related theories of atoms and molecules....Pages 263-301 Front Matter....Pages 261-261 The Hartree-Fock Theory for Coulomb Systems....Pages 303-312 There Are No Unfilled Shells in Unrestricted Hartree-Fock Theory....Pages 313-315 Many-Body Atomic Potentials in Thomas—Fermi Theory....Pages 317-328 The Positivity of the Pressure in Thomas Fermi Theory....Pages 329-354 The Thomas—Fermi—von Weizsäcker Theory of Atoms and Molecules....Pages 357-370 Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom Without Electron Repulsion....Pages 371-381 The most negative ion in the Thomas—Fermi—von Weizsäcker theory of atoms and molecules....Pages 383-397 Front Matter....Pages 399-399 Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter....Pages 401-404 Stability of Coulomb Systems with Magnetic Fields....Pages 405-424 Stability of Coulomb Systems with Magnetic Fields....Pages 425-436 Stability of Matter in Magnetic Fields....Pages 437-441 The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics....Pages 443-470 One-Electron Relativistic Molecules with Coulomb Interaction....Pages 471-484 The Stability and Instability of Relativistic Matter....Pages 485-521 Stability of Relativistic Matter via Thomas—Fermi Theory....Pages 523-533 Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields....Pages 535-557 Front Matter....Pages 559-559 The stability of matter....Pages 561-577 Existence of Thermodynamics for Real Matter with Coulomb Forces....Pages 579-582 The Thermodynamic Limit for Jellium....Pages 583-602 Front Matter....Pages 605-605 Self-Energy of Electrons in Non-Perturbative QED....Pages 607-623 Front Matter....Pages 605-605 Renormalization of the Regularized Relativistic Electron-Positron Field....Pages 625-635 Ground states in non-relativistic quantum electrodynamics....Pages 637-675 Front Matter....Pages 677-677 Bosonic Systems....Pages 679-680 Ground State Energy of the Low Density Bose Gas....Pages 681-684 Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional....Pages 685-697 The Bose Gas: A Subtle Many-Body Problem....Pages 699-719 The N 5/3 Law For Bosons....Pages 721-723 The N 7/5 Law for Charged Bosons....Pages 725-756 Ground State Energy of the One-Component Charged Bose Gas....Pages 757-793 Back Matter....Pages 797-812 This collection of papers -- starting with a brilliant article by one of the masters of the field -- gives an excellent current review of our knowledge of matter. Partially basing his work on a variational formulation of quantum mechanics, E.H. Lieb links the difficult question of the stability of matter with important problems in functional analysis. In this collection the reader will find general results together with deep insights into quantum systems combined with papers on the structure of atoms and molecules, the thermodynamic limit, and stellar structures. The book is suitable as an accompanying text for a graduate course in quantum mechanics. In this new edition two new sections have been added: Section 7 contains papers on quantum electrodynamics, and Section 8 on Boson systems. . This collection of papers - starting with a brilliant article by one of the masters of the field - gives an excellent current review of our knowledge of matter. Partially basing his work on a variational formulation of quantum mechanics, E.H. Lieb links the difficult question of the stability of matter with important problems in functional analysis. In this collection the reader will find general results together with deep insights into quantum systems combined in papers on the structure of atoms and molecules, the thermodynamic limit, and stellar structure. The book is suitable as an accompanying text for a graduate course in quantum mechanics. This new edition contains significant new results on matter in magnetic fields.