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A Method for Studying Model Hamiltonians: A Minimax Principle for Problems in Statistical Physics centers on methods for solving certain problems in statistical physics which contain four-fermion interaction. Organized into four chapters, this book begins with a presentation of the proof of the asymptotic relations for the many-time correlation functions. Chapter 2 details the construction of a proof of the generalized asymptotic relations for the many-time correlation averages. Chapter 3 explains the correlation functions for systems with four-fermion negative interaction. The last chapter shows the model systems with positive and negative interaction components.

Concise monograph devoted to techniques of solving many-body problems in physics using the quantum-mechanical Green function method. Requires some familiarity with the basic theory of quantum mechanics and statistical mechanics. 1962 edition.

This book is an English translation of a collection of papers in Russian from a conference held in Moscow and St. Petersburg in 1983, 200 years after Euler's death. Two of the Russian papers in the collection are themselves translations from the German. The present English translation appears in 2007, 300 years after his birth. We speak of the ""Age of Euler"". A justification of this term is provided by a list of scientific terms connected with Euler s name and his many contributions to pure mathematics, well-known in the mathematical community and, in part, covered in this volume. What makes this collection remarkable, though, is the extensive treatment of Euler's contributions outside pur...

In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles. Contents:On the Theory of SuperfluidityQuasi-Averages in Problems of Statistical MechanicsHydrodynamics Equations in Statistical MechanicsO...

Le projet de ce livre etait une gageure. lIs' agissait de rendre compte du developpement des mathematiques depuis cinquante ans a un public mathematique aussi large que possi ble, sans viser l'exhaustivite, mais sans se bomer a un apen;u superticiel. Pour tenter de realiser cette ambition, Ie comite de lecture a fait appel a des mathematiciens actifs dans divers domaines des mathematiques. II a recru une trentaine de contributions qui forment la matiere de ce livre. En outre, il a auditionne plusieurs mathematiciens qui donnent leur point de vue personnel. Entin il a reuni quelques documents, soit statistiques, soit bibliographiques, pour completer les references donnees par les auteurs et s...

This volume contains articles covering a wide range of current directions in modern statistical mechanics and dynamical systems theory. Scientists, researchers, and students working in mathematical physics and statistical mechanics will find this book of great interest. Among the topics covered are: phase transition problems, including superconductivity and superfluidity; methods of nonequilibrium statistical mechanics and fluctuation theory; quantum collective phenomena; superradiance; spin glasses; polaron problems; chains of Bogolyubov equations and kinetic equations; algebraic aspects of quantum-dynamical semigroups; the collective variables method; and qualitative properties of classical dynamical systems."

The majority of the "memorable" results of relativistic quantum theory were obtained within the framework of the local quantum field approach. The explanation of the basic principles of the local theory and its mathematical structure has left its mark on all modern activity in this area. Originally, the axiomatic approach arose from attempts to give a mathematical meaning to the quantum field theory of strong interactions (of Yukawa type). The fields in such a theory are realized by operators in Hilbert space with a positive Poincare-invariant scalar product. This "classical" part of the axiomatic approach attained its modern form as far back as the sixties. * It has retained its importance ...