This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.
This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear)...
This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre- sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in- finite systems, which are described by infinite...
This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical St...
This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris. Its title accurately reflects the domains to which Yvonne Choquet-Bruhat has made essential contributions. Since the rise of General Relativity, the geometry of Manifolds has become a non-trivial part of space-time physics. At the same time, Functional Analysis has been of enormous importance in Quantum Mechanics, and Quantum Field Theory. Its role becomes decisive when one...
This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, ...
This volume presents the lectures given by distinguished contributors at the First German-Polish Max Born Symposium, held at Wojnowice in Poland in September, 1991. This is the first such symposium to continue the tradition of a German-Polish collaboration in theoretical physics in the form of biannual seminars organized between the Universities of Leipzig and Wroclaw since the early seventies. The papers in this volume are devoted to quantum group theory, noncommutative differential geometry, and integrable systems. Particular emphasis is given to the formalism of noncommutative geometry on...
This volume presents the lectures given by distinguished contributors at the First German-Polish Max Born Symposium, held at Wojnowice in Poland in Se...
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn t require the use of divergent quantities and works on a large class of Lorenzian manifolds.
We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity.
pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a...
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of pertur...
Material particles, electrons, atoms, molecules, interact with one another by means of electromagnetic forces. That is, these forces are the cause of their being combined into condensed (liquid or solid) states. In these condensed states, the motion of the particles relative to one another proceeds in orderly fashion; their individual properties as well as the electric and magnetic dipole moments and the radiation and absorption spectra, ordinarily vary little by comparison with their properties in the free state. Exceptiotls are the special so-called collective states of condensed media that...
Material particles, electrons, atoms, molecules, interact with one another by means of electromagnetic forces. That is, these forces are the cause of ...
This book presents the text of most of the lectures which were de- livered at the Meeting Quantum Theories and Geometry which was held at the Fondation Les Treilles from March 23 to March 27, 1987. The general aim of this meeting was to bring together mathemati- cians and physicists who have worked in this growing field of contact between the two disciplines, namely this region where geometry and physics interact creatively in both directions. It 1S the strong belief of the organizers that these written con- tributions will be a useful document for research people workin~ 1n geometry or...
This book presents the text of most of the lectures which were de- livered at the Meeting Quantum Theories and Geometry which was held at the Fondatio...
to our own also needs to be understood. Such unification may also require that the supersymmetry group possess irreducible representations with infinite reductiori on the Poincare subgroup, to accommodate an infinite set of particles. Such possibilities were 5 envisaged long ago and have recently reappeared in Kaluza-Klein . 6 d' . th 7 S . l' th supergraVlty an m superstnng eory. upersymmetry Imp Ies at forces that are mediated by bose exchange must be complemented by forces that are due to the exchange of fermions. The masslessness of neutrinos is suggestive-we continue to favor the idea...
to our own also needs to be understood. Such unification may also require that the supersymmetry group possess irreducible representations with infini...
Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pOinted out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators a. ffiliated to such rings. The absence of power tools in functional analysis - mainly settled in their...
Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unso...
