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Book review

Author(s) Albeverio, S. (ed.)
Blanchard, Ph. (ed.)
Testard, D. (ed.)
Title Stochastics, algebra and analysis in classical and quantum dynamics
Publisher Kluwer
Year of publication 1990
Reviewed by Günter Vojta

This book contains the proceedings of the Fourth French-German Encounters on Mathematics and Physics at the Centre International de Recherches Mathematiques, Marseille, 1988. These encounters were again devoted to the interaction between mathematics and physics which has proved to be of growing importance during the last decades. Highly interesting themes are treated in 14 papers, mostly written in English and partly of introductory or review character. The topics treated range from integrable dynamical systems of classical Hamiltonian mechanics and solitary waves to quantum field theory, strings and white noise.

Particularly interesting is a full introduction by D. Kastler to entire cyclic cohomology of graded Banach spaces (78 pp.), a mathematical subject motivated by quantum physics where superalgebras abound due to the parallel occurence of bosonic and fermionic degrees of freedom. Other contributions are engaged in the two-dimensional Ginzburg-Landau theory for superconductors, in a new differential calculus on Poisson space, in dynamical systems of plasma theory, in reaction-diffusion models, and in the simulation of epidemic dynamics. Further, reflections on stochastic analysis and mathematical structures by P. Kree are worth mentioning. The volume is produced from different original typescripts. An index of one page seems too short.

Altogether, this proceedings gives again a multitude of valuable scientific information on a professional level. The book is certainly of interest for a variety of experts, teachers and students of mathematical and theoretical physics and of stochastic analysis, among others. It can be recommended for libraries.