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WORLD SCIENTIFIC eBooks

XVIIth International Congress on Mathematical Physics

Arne Jensen

Published Dec 20, 2012• 26 citations

Abstract

The International Congress on Mathematical Physics is a major conference in its field that attracts a very wide spectrum of researchers. Held every three years, it provides an overview of recent developments and achievements in mathematical physics. This volume presents the plenary lectures and invited topical session lectures from the XVIIth ICMP, which was held in Aalborg, Denmark, August 2012. It also includes additional material from the Congress. In this volume, one can find survey lectures on orthogonal polynomials, random systems, information theory in physics, several aspects of quantum field theory and quantum mechanics, general relativity, and classical and quantum dynamical systems. The topical sessions covered the following areas: •Dynamical systems, classical and quantum •Equilibrium and non-equilibrium statistical mechanics •PDE and general relativity •Stochastic models and probability •Operator algebras, exactly solvable models •Quantum mechanics and spectral theory •Quantum information and computation •Quantum many-body theory and condensed matter physics •Quantum field theory •String theory and quantum gravity Readers are exposed to state-of-the-art views on mathematical physics. Several of the plenary lectures give broad surveys on recent activities, for example, in orthogonal polynomials, PDE in mathematical physics, and information theory in physics.

DOI: 10.1142/8700

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This book is the first volume of the proceedings of the Canadian Mathematical Society Annual Seminar on Mathematical Quantum Theory, held in Vancouver in August 1993. The seminar was run as a research-level summer school concentrating on two related areas of contemporary mathematical physics. The subject of the first session, quantum field theory and many-body theory, is covered in the present volume; papers from the second session, on Schr odinger operators, are in Volume 2. Each session featured a series of minicourses, consisting of approximately four one-hour lectures, designed to introduce students to current research in a particular area. In addition, about thirty speakers gave one-hour expository lectures. With contributions by some of the top experts in the field, this book provides an overview of the state of the art in mathematical quantum field and many-body theory.

The present volume contains contributions of the 32nd International Conference on Quantum Probability and Related Topics held in Levico Terme (Italy) in June 2011 as the annual meeting of the Association for Quantum Probability and Innite Dimensional Analysis (AQPIDA). The\nconference was sponsored by CIRM Bruno Kessler Foundation, Centro V. Volterra and MIUR PRIN 2009 project "Quantum Probability and Applications\nto Information Theory".\nThe goal of the conference was to communicate new results in quantum probability and infinite dimensional analysis and related elds. A wide range of topics was discussed: white noise and higher powers of white\nnoise, quantum Markov semigroups and applications to quantum statistical mechanics, quantum stochastic calculus, stochastic differential equations, quantum Levy processes, product systems and interacting Fock spaces, algebraic probability, realizations of classical processes, quantum probability in bio-systems, complexity, entanglement and measurement showing the highly interdisciplinary activity of the field and deep connections with many areas of mathematics.\nSelected contributions highlighting the latest developments, collected after the conference, refereed by one or more experts, are now presented in this volume that will be of great value for researchers, applied mathematicians and graduate students.

This work contains the proceedings of the International Conference on Mathematical Results in Quantum Mechanics held in Blossin, Germany, May 17-21, 1993. It aims to draw attention to the recent developments in quantum mechanics and related mathematical problems. The book features sections not only on traditional subjects such as Schroedinger and Dirac operators and generalized Schroedinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications.

These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled Scattering Theory in Mathematics and Physics held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.