The Stability of Matter: From Atoms to Stars

With this book, Elliott Lieb joins his peers Hermann Weyl and Chen Ning Yang. Weyl's Selecta was published in 1956, Yang's Selected Papers in 1983. Lieb's "Selecta", like its predecessors, gives us the essence of a great mathema­ tical physicist concentrated into one convenient volume. Weyl, Yang and Lieb have much more in common than the accident of this manner of publication. They have in common a style and a tradition. Each of them is master of a for­ midable mathematical technique. Each of them uses hard mathematical ana­ lysis to reach an understanding of physical laws. Each of them enriches both physics and mathematics by finding new mathematical depths in the description of familiar physical processes. The central theme of Weyl's work in mathematical physics was the idea of symmetry, linking physical invariance-principles with the mathematics of group-theory. One of Yang's central themes is the idea of a gauge field, linking physical interactions with the mathematics of fibre-bundles. The central theme of Lieb's papers collected in this book is the classical Thomas-Fermi model of an atom, linking the physical stability of matter with the mathematics of func­ tional analysis. In all three cases, a rather simple physical idea provided the starting-point for building a grand and beautiful mathematical structure. Weyl, Yang and Lieb were not content with merely solving a problem. Each of them was concerned with understanding the deep mathematical roots out of which physical phenomena grow.

I. Review.- I.1 The Stability of Matter: From Atoms to Stars.- II. Exact Results on Atoms.- II.1 Lower Bound to the Energy of Complex Atoms.- II.2 Improved Lower Bound on the Indirect Coulomb Energy.- II.3 Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates.- II.4 Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle.- II.5 Atomic and Molecular Negative Ions.- II.6 Bound on the Maximum Negative Ionization of Atoms and Molecules.- II.7 Asymptotic Neutrality of Large-Z Ions.- II.8 Universal Nature of van der Waals Forces for Coulomb Systems.- II.9 Approximate Neutrality of Large-Z Ions.- III. General Results with Applications to Atoms.- III.1 Kinetic Energy Bounds and Their Application to the Stability of Matter.- III.2 Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities.- III.3 On Semi-Classical Bounds for Eigenvalues of Schrodinger Operators.- III.4 The Number of Bound States of One-Body Schrodinger Operators and the Weyl Problem.- 111.5 Variational Principle for Many-Fermion Systems.- IV. Thomas-Fermi and Related Theories.- IV.1 Thomas-Fermi and Related Theories of Atoms and Molecules.- IV.2 The Hartree-Fock Theory for Coulomb Systems.- IV.3 Many-Body Atomic Potentials in Thomas-Fermi Theory.- IV.4 The Positivity of the Pressure in Thomas-Fermi Theory.- IV.5 The Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules.- IV.6 Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom Without Electron Repulsion.- IV.7 The Most Negative Ion in the Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules.- V. Stability of Matter.- V.1 Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter.- V.2 The N5/3 Lawfor Bosons.- V.3 Stability of Coulomb Systems with Magnetic Fields. I. The One-Electron Atom.- V.4 Stability of Coulomb Systems with Magnetic Fields. II. The Many-Electron Atom and the One-Electron Molecule.- V.5 The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics.- V.6 A Rigorous Examination of the Chandrasekhar Theory of Stellar Collapse.- V.7 The Stability and Instability of Relativistic Matter.- V.8 Many-Body Stability Implies a Bound on the Fine-Structure Constant.- V.9 The N7/5 Law for Charged Bosons.- V.10 One-Electron Relativistic Molecules with Coulomb Interaction.- VI. The Thermodynamic Limit for Real Matter with Coulomb Forces.- VI.1 The Stability of Matter.- VI.2 Existence of Thermodynamics for Real Matter with Coulomb Forces.- VI.3 Lectures on the Thermodynamic Limit for Coulomb Systems.- VI.4 The Thermodynamic Limit for Jellium.- Publications of Elliott H. Lieb.