From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l'Institut d'Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan­ tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.

From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l''Institut d''Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan­ tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.

The first international conference on. relativity physics and parallel computing took place February 24-28, 1986, at the International Institute of Theoretical Physics at Utah State University in Logan, Utah. Before proceeding to summarize some of the main points of the conference I would like to make a few remarks about the goals of the International Institute of Theoretical Physics. The Institute undertakes frontier research in both pure and applied physics and is housed in the new physics building at Utah State University. The applied research is in solar energy and optical parallel computing. We are in the midst of building four very efficient solar collectors and, in the very near future, parts of an optical parallel computer in the Institute. The pure research is concerned with relativity physics, particle physics, condensed matter physics, quantum systems, etc. On the macroscop­ ic level, we are concerned with possible experimental tests of Einstein''s General Relativity. On the microscopic level, we are interested in the unification of gravitation with the other interactions. In addition to research, the International Institute sponsors visiting scientists and en­ courages collaborations, etc.

The first international conference on. relativity physics and parallel computing took place February 24-28, 1986, at the International Institute of Theoretical Physics at Utah State University in Logan, Utah. Before proceeding to summarize some of the main points of the conference I would like to make a few remarks about the goals of the International Institute of Theoretical Physics. The Institute undertakes frontier research in both pure and applied physics and is housed in the new physics building at Utah State University. The applied research is in solar energy and optical parallel computing. We are in the midst of building four very efficient solar collectors and, in the very near future, parts of an optical parallel computer in the Institute. The pure research is concerned with relativity physics, particle physics, condensed matter physics, quantum systems, etc. On the macroscop­ ic level, we are concerned with possible experimental tests of Einstein's General Relativity. On the microscopic level, we are interested in the unification of gravitation with the other interactions. In addition to research, the International Institute sponsors visiting scientists and en­ courages collaborations, etc.

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im­ portant mathematical works on the arena of supergravity has taken place, starting with Kostant's theory of graded manifolds and continuing with Batchelor's work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path­ integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe­ maticians and relativists who bring their experience in differen­ tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super­ symmetry is its relationship to the elementary particle spectrum.

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im­ portant mathematical works on the arena of supergravity has taken place, starting with Kostant''s theory of graded manifolds and continuing with Batchelor''s work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path­ integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe­ maticians and relativists who bring their experience in differen­ tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super­ symmetry is its relationship to the elementary particle spectrum.

From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l'Institut d'Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan­ tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.

From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l''Institut d''Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan­ tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.

The first international conference on. relativity physics and parallel computing took place February 24-28, 1986, at the International Institute of Theoretical Physics at Utah State University in Logan, Utah. Before proceeding to summarize some of the main points of the conference I would like to make a few remarks about the goals of the International Institute of Theoretical Physics. The Institute undertakes frontier research in both pure and applied physics and is housed in the new physics building at Utah State University. The applied research is in solar energy and optical parallel computing. We are in the midst of building four very efficient solar collectors and, in the very near future, parts of an optical parallel computer in the Institute. The pure research is concerned with relativity physics, particle physics, condensed matter physics, quantum systems, etc. On the macroscop­ ic level, we are concerned with possible experimental tests of Einstein''s General Relativity. On the microscopic level, we are interested in the unification of gravitation with the other interactions. In addition to research, the International Institute sponsors visiting scientists and en­ courages collaborations, etc.

The first international conference on. relativity physics and parallel computing took place February 24-28, 1986, at the International Institute of Theoretical Physics at Utah State University in Logan, Utah. Before proceeding to summarize some of the main points of the conference I would like to make a few remarks about the goals of the International Institute of Theoretical Physics. The Institute undertakes frontier research in both pure and applied physics and is housed in the new physics building at Utah State University. The applied research is in solar energy and optical parallel computing. We are in the midst of building four very efficient solar collectors and, in the very near future, parts of an optical parallel computer in the Institute. The pure research is concerned with relativity physics, particle physics, condensed matter physics, quantum systems, etc. On the macroscop­ ic level, we are concerned with possible experimental tests of Einstein's General Relativity. On the microscopic level, we are interested in the unification of gravitation with the other interactions. In addition to research, the International Institute sponsors visiting scientists and en­ courages collaborations, etc.

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im­ portant mathematical works on the arena of supergravity has taken place, starting with Kostant's theory of graded manifolds and continuing with Batchelor's work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path­ integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe­ maticians and relativists who bring their experience in differen­ tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super­ symmetry is its relationship to the elementary particle spectrum.

Over the past five years, through a continually increasing wave of activity in the physics community, supergravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the spectrum of elementary particles. Concurrently im­ portant mathematical works on the arena of supergravity has taken place, starting with Kostant''s theory of graded manifolds and continuing with Batchelor''s work linking this with the superspace formalism. There remains, however, a gap between the mathematical and physical approaches expressed by such unanswered questions as, does there exist a superspace having all the properties that physicists require of it? Does it make sense to perform path­ integral in such a space? It is hoped that these proceedings will begin a dialogue between mathematicians and physicists on such questions as the plan of renormalisation in supergravity. The contributors to the proceedings consist both of mathe­ maticians and relativists who bring their experience in differen­ tial geometry, classical gravitation and algebra and also quantum field theorists specialized in supersymmetry and supergravity. One of the most important problems associated with super­ symmetry is its relationship to the elementary particle spectrum.