Synopses & Reviews
These volumes contain a collection of essays by many of the closest co-workers of Raphael Hoegh-Krohn (1938-1988), one of the outstanding mathematical physicists of our age. The contributions vary in style, purpose, and content--some are surveys that summarize and clarify a subject area, others are new and adventurous expeditions into unknown territory. The topics cover most aspects of modern mathematical physics with special emphasis on methods from operator theory and stochastic analysis. Volume 1 contains papers on mathematical analysis (both linear and nonlinear), stochastics, and applications. Volume 2 discusses mathematical problems in quantum and statistical physics.
Synopsis
A collection of essays by many of the closest co-workers of Raphael H
Table of Contents
Preface; Part I. Quantum Mechanics: 1. On the low density of Boson models: Langevin equation; 2. Schrödinger operators with potentials supported by null sets; 3. Landau Hamiltonians on symmetric spaces; 4. Renormalization group analysis and quasicrystals; 5. The measurement problem in the stochastic formulation of quantum mechanics; 6. Schrödinger operators at threshold; 7. Spectral analysis and scattering theory for Schrödinger operators with an interaction supported by a regular curve; 8. Lattice models of solids; 9. Schrödinger operators on unusual manifolds; 10. High energy resolvent estimates for Schrödinger operators; 11. Point interactions as solvable models; 12. Stochastic model of quantum mechanics; Part II. Quantum Field Theory: 13. Maximality of infinite dimensional Dirichlet forms and Høegh-Krohn's model of quantum fields; 14. Global Markov property in quantum field theory and statistical mechanics: a review on results and problems; 15. Hypercontractivity: a bibliographic review; 16. Progress and problems in algebraic quantum field theory; 17. Høegh-Krohn's model of quantum fields and the absolute continuity of measures; 18. Baryon states in lattice QCD; 19. The energy of a Weyl soliton; Part III. Statistical Physics: 20. Morphology and classification of galaxies: a stochastic model; 21. Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction; 22. Verification of the global Markov property for strongly coupled trigonometric interactions; 23. Decomposition of Ising models and the Mayer expansion; 24. Towards time-dynamics for bosonic systems in quantum statistical mechanics.