## The Stability of Matter: From Atoms to Stars: Selecta of Elliott H. LiebThe 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. |

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### Contents

III | 11 |

IV | 61 |

V | 63 |

VI | 65 |

VII | 79 |

VIII | 83 |

IX | 87 |

X | 91 |

XXXI | 383 |

XXXII | 399 |

XXXIII | 401 |

XXXIV | 405 |

XXXV | 425 |

XXXVI | 437 |

XXXVII | 443 |

XXXVIII | 471 |

XI | 103 |

XII | 113 |

XIII | 121 |

XIV | 127 |

XV | 147 |

XVI | 171 |

XVII | 191 |

XVIII | 193 |

XIX | 205 |

XX | 241 |

XXI | 245 |

XXII | 257 |

XXIII | 261 |

XXIV | 263 |

XXV | 303 |

XXVI | 313 |

XXVII | 317 |

XXVIII | 329 |

XXIX | 357 |

XXX | 371 |

XXXIX | 485 |

XL | 523 |

XLI | 535 |

XLII | 559 |

XLIII | 561 |

XLIV | 579 |

XLV | 583 |

XLVI | 605 |

XLVII | 607 |

XLVIII | 625 |

XLIX | 637 |

L | 677 |

LI | 681 |

LII | 685 |

LIII | 699 |

LIV | 721 |

LV | 725 |

LVI | 757 |

LVII | 797 |

### Common terms and phrases

assume asymptotic atom ball Benguria Bose Gas bosons Charged Bosons consider constant convergence convex Coulomb potential decreasing defined denote density density matrix Dirac Dirac operator Dyson E. H. Lieb eigenvalues electrons Elliott H Elliott Lieb equation exists fact fermions finite fixed given ground state energy ground-state Hamiltonian Hartree-Fock Hence implies inequality infimum infinity integral interaction jellium kinetic energy Lemma Lett lower bound magnetic field many-body Math mathematical minimizing molecules monotone negative neutral non-negative Note nuclear charge nuclei obtain operator particle number Phys Physics positive Princeton problem proof of Theorem prove quantum dots quantum mechanics radius relativistic Remark replaced repulsion result right side satisfies Schrodinger Sect sequence Solovej solution spherically symmetric stability of matter term TF theory thermodynamic limit Thirring Thomas-Fermi theory unique upper bound vector wave function zero