Contents Part 1. Quantu m Field Theory, Statistical Mechanics, and Nonrelativistic Quantu m System s Preface ix A Mathematical Genealogy xiii A Selection of Barry Stories xvii Quantum Field Theory, Statistical Mechanics Perspectives in Statistical Mechanics MICHAEL AIZENMAN 3 Coherent Infrared Representations in Non-Relativistic QED THOMAS CHEN and JURG FROHLICH 25 Quantum Spin Systems After DLS 1978 BRUNO NACHTERGAELE 47 Barry Simon's Contributions to Quantum Field Theory LON ROSEN 69 Nonrelativistic Two-Body and iV-Body Quantum Systems, Resonances Isoperimetric Inequalities for Eigenvalues of the Laplacian MARK S. ASHBAUGH and RAFAEL D. BENGURIA 105 Non-Self-Adjoint Operators and Pseudospectra E. B. DAVIES 141 Barry Simon's Contributions to Non-Relativistic Quantum Mechanics: Two-Body and A^-Body Schrodinger Operators and Resonances RICHARD FROESE 153 N-Body Quantum Scattering and Quantum Resonances: An Overview CHRISTIAN GERARD 169 Mathematical Analysis of Born-Oppenheimer Approximations GEORGE A. HAGEDORN and ALAIN JOYE 203
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