This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.

- A collection of papers spanning decades and touching on a wide variety of research topics on modern theoretical physics written by leading scientists from the Belarusian State University bull; Provides concise information about the methods and applicati.

The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.

Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up- to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.

Quantum systems in all areas of physics, from atomic and molecular physics, nuclear and particle physics to condensed matter and astrophysics, provide a rich mosaic of different structures. Yet there are some simple and universal working principles of nature which seem to govern these structures and manifest themselves in various forms, as well as likely hypothetical ones which might do the same. For example, the same symmetry group structure occurs again and again in optics, atomic physics and particle physics. Concepts like potential, phases, bound states, tunneling, interference, solitons, radiation and resonance are universal.It is for those reasons that a collection of recent works in the many areas of physics on quantum structures and the methods for their investigation is important. The present volume fulfills this task to a large extent. The contributions are wide-ranging and yet there is a certain continuity. The main topics, namely non-perturbative methods in quantum theory, quantum nonlinear systems, quantum phases and magnetic monopoles, are covered by longer review articles and are enriched by many related contributions. It is also very appropriate that the corresponding mathematical methods, such as those for solving Schrödinger and relativistic wave equations, as well as those of algebra and group representations and analysis, are included in this volume.