A. Jaffe – författare

The energy reserves of the Caspian Region have been hailed as the new ''Middle East''. This book offers a thorough assessment of its energy resources and the nature of the international politics that surround them. This volume presents a unique study of the various dimensions of Caspian energy, ranging from the geopolitical to the economic, technical, religious and political.

The energy reserves of the Caspian Region have been hailed as the new 'Middle East'. This book offers a thorough assessment of its energy resources and the nature of the international politics that surround them. This volume presents a unique study of the various dimensions of Caspian energy, ranging from the geopolitical to the economic, technical, religious and political.

The energy reserves of the Caspian Region have been hailed as the new 'Middle East'. This book offers a thorough assessment of its energy resources and the nature of the international politics that surround them. This volume presents a unique study of the various dimensions of Caspian energy, ranging from the geopolitical to the economic, technical, religious and political.

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.

This book is addressed to one problem and to three audiences. The problem is the mathematical structure of modem physics: statistical physics, quantum mechanics, and quantum fields. The unity of mathemati­ cal structure for problems of diverse origin in physics should be no surprise. For classical physics it is provided, for example, by a common mathematical formalism based on the wave equation and Laplace''s equation. The unity transcends mathematical structure and encompasses basic phenomena as well. Thus particle physicists, nuclear physicists, and con­ densed matter physicists have considered similar scientific problems from complementary points of view. The mathematical structure presented here can be described in various terms: partial differential equations in an infinite number of independent variables, linear operators on infinite dimensional spaces, or probability theory and analysis over function spaces. This mathematical structure of quantization is a generalization of the theory of partial differential equa­ tions, very much as the latter generalizes the theory of ordinary differential equations. Our central theme is the quantization of a nonlinear partial differential equation and the physics of systems with an infinite number of degrees of freedom. Mathematicians, theoretical physicists, and specialists in mathematical physics are the three audiences to which the book is addressed. Each of the three parts is written with a different scientific perspective.

The importance of gauge theory for elementary particle physics is by now firmly established. Recent experiments have yielded convincing evidence for the existence of intermediate bosons, the carriers of the electroweak gauge force, as well as for the presence of gluons, the carriers of the strong gauge force, in hadronic inter­actions. For the gauge theory of strong interactions, however, a number of important theoretical problems remain to be definitely resolved. They include the quark confinement problem, the quantita­tive study of the hadron mass spectrum as well as the role of topology in quantum gauge field theory. These problems require for their solution the development and application of non-perturbative methods in quantum gauge field theory. These problems, and their non-perturbative analysis, formed the central interest of the 1983 Cargese summer institute on "Progress in Gauge Field Theory. " In this sense it was a natural sequel to the 1919 Cargese summer institute on "Recent Developments in Gauge Theories. " Lattice gauge theory provides a systematic framework for the investigation of non-perturbative quantum effects. Accordingly, a large number of lectures dealt with lattice gauge theory. Following a systematic introduction to the subject, the renormalization group method was developed both as a rigorous tool for fundamental questions, and in the block-spin formulation, the computations by Monte Carlo programs. A detailed analysis was presented of the problems encountered in computer simulations. Results obtained by this method on the mass spectrum were reviewed.