Mathematical problems in theoretical physics. International conference held in Rome, June 6--15, 1977
There are 34 main lectures and 7 short communications in this volume. Leading specialists in mathematical physics and related topics contributed lectures for this volume (A. Jaffe, K. Osterwalder, E. Lieb, H. Araki, D. Kastler, J. Combes, M. Atiyah, S. Novikov, V. Zakharov, S. Albeverio, Ya. Sinai, P. Calogero, R. Dobrushin, D. Ruelle, R. Temam, W. Thirring to mention a few. The questions under discussion are rather diverse. They include constructive quantum field theory, lattice gauge theories, phase transitions, operator algebras, analysis on manifolds and topology in quantum field theory, solitons and inverse scattering techniques, statistical physics, turbulence and asymptotic behavior of dynamical systems and Navier-Stokes equations. The mathematical interesting papers will be reviewed individually. In the whole this collection gives an up to date report on the recent developments in some important parts of mathematical physics and provides references for those who are going to work in these fields. Table of Contents: Arthur Jaffe, Lattice instantons: What they are and why they are important (3--13); Gian Fabrizio De Angelis, Gauge fields on the lattice (14--25); K. Osterwalder, E. Seiler, Lattice gauge theories (26--36); Jürg Fröhlich, Some frontiers in constructive quantum field theory and equilibrium statistical mechanics (37--58); Elliott H. Lieb, New proofs of long range order (59--67); Joel L. Lebowitz, Number of phases in one component ferromagnets (68--80); John E. Roberts, A survey of local cohomology (81--93) [Zbl 0449.55009]; Huzihiro Araki, Operator algebras and statistical mechanics (94--105) [Zbl 0436.46055]; Daniel Kastler, Foundations of equilibrium quantum statistical mechanics (106--123) [Zbl 0433.46060]; Ola Bratteli, Richard H. Herman, Unbounded derivations of \(C^*\)-algebras and corresponding dynamics (124--133) [Zbl 0429.46038]; Masamichi Takesaki, Introduction to the flow of weights on factors of type II (134--144) [Zbl 0463.46051]; Alain Connes, The von Neumann algebra of a foliation (145--151) [Zbl 0433.46056]; Edward G. Effros, Nuclearity and the \(C^*\)-algebraic flip (152--160) [Zbl 0431.46043]; Dorte Olesen, On the Connes spectrum of simple \(C^*\)-dynamical systems (161--170) [Zbl 0436.46053]; Detlev Buchholz, Quantum field theory of massless particles and scattering theory (171--182); J. M. Combes, Scattering theory in quantum mechanics and asymptotic completeness (183--204) [Zbl 0435.47010]; L. O'Raifeartaigh, Static solitons in more than one dimension (205--215); F. Atiyah, Geometry of Yang-Mills fields (216--221); S. P. Novikov, Periodic solitons and algebraic geometry (222--228); A.A. Belavin, V.E. Zakharov, Yang-Mills equations as inverse scattering problem (229--234); F. Calogero, Nonlinear evolution equations solvable by the inverse spectral transform (235--269) [Zbl 0435.35070]; L. D. Faddeev, P. P. Kulish, Quantization of particle-like solutions in field theory (270--278); Sergio Albeverio, Raphael Høegh-Krohn, Topics in infinite dimensional analysis (279--302) [Zbl 0442.28018]; Ya. G. Sinai, Mathematical foundations of the renormalization group method in statistical physics (303--311); P. Collet, J. P. Eckmann, On the renormalization group for the hierarchical model (312--312); Richard S. Ellis, Charles M. Newman, Fluctuationes in Curie-Weiss exemplis (313--324); R. L. Dobrushin, Yu. M. Suhov (Sukhov), On the problem of the mathematical foundation of the Gibbs postulate ie classical statistical mechanics (325--340) [Zbl 0439.70016]; David Ruelle, Dynamical systems with turbulent behavior (341--360) [Zbl 0452.34038]; R. Temam, Generic properties of Navier-Stokes equations (361--370) [Zbl 0428.35065]; H. Kesten, G. C. Papanicolaou, A limit theorem for turbulent diffusion 371--374) [Zbl 0431.34043]; M. C. Polivanov, Many particle scattering amplitudes (375--385); I.V. Tutin, O.I. Zavialov, A Remark on equations of motion in asymptotically free theories (386--389); S. A. Anikin, C. I. Zavialov, Short-distance expansion for products of current-like operators (390--394); W. Thirring, The use of exterior forms in field theory (395--402) [Zbl 0449.53052]; Michael Aizenman, On extensions of flows in the presence of sets of singularities (405--414) [Zbl 0428.28012]; J. Bricmont, J.R. Fontaine, L. Landau, On the uniqueness of the equilibrium state for plane rotators (415--416); E. A. Tagirov, I. T. Todorov, A geometric approach to the solution of conformal invariant field equations (417--419); Alberto Frigerio, Vittorio Gorini, Maurizio Verri, Stability, detailed balance and KMS condition for quantum systems (420--425) [Zbl 0428.46057]; Gérard G. Emch, Stochasticity and irreversibility in infinite mechanical systems (426--432) [Zbl 0429.46044]; W. Pusz, Why the KMS states? (433--435) [Zbl 0436.46057]; G. Gallavotti, F. Guerra, S. Miracle-Solés, A comment to the talk by E. Seiler (436--438).
stochastic behavior of dynamical systems
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