Quantum Field Theory: Two-Dimensional Integrable Systems, Exact S-Matrices, and Nonlocal Field Theories

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The research, in the general area of theoretical elementary particle physics, will concentrate on aspects of two-dimensional quantum field theory which are important in the solution of mathematical problems that arise in the understanding of superstring theory and statistical systems. (Super)string theory, which is believed to provide the basic understanding of the fundamental forces of nature, has as its underlying mathematical and quantum-mechanical description the formalism and methods of two-dimensional quantum field theory. The same formalism and methods are used in the study of certain one- and two-dimensional statistical mechanics models which describe the behavior of diverse systems such as long- chain molecules and membranes, and may explain certain phenomena such as high temperature superconductivity. In both cases it has become apparent that much progress can be made in those situations where one is dealing with "integrable" systems, because in such situations a complete solution of the corresponding mathematical problems can be obtained. It is believe that the relevant integrable systems can be described in two complementary, but equivalent, manners, either as so- called Liouville and Toda theories, or as nonlocal induced gravity and W-gravity theories. The research will focus on the study of such theories and is expected to provide important information concerning strings and the explanation of the fundamental forces of nature, as well as information about statistical systems which arise in many practical applications.