This proposal requests funds to permit Dr. So-Young Pi, Department of Physics, Boston University to pursue with Dr. Kwang Sup Soh, Department of Physics, Seoul National University, for a period of 24 months, a program of cooperative research on equilibrium and non-equilibrium quantum field theory in curved space-time in the Schrodinger picture. Quantum field theory will be studied in curved space-times, such as Schwarzschild and Kerr black hole manifolds, Einstein and de Sitter universes, and other anisotropic models which are relevant to the very early universe. This project is particularly relevant to many cosmological models where symmetry breaking and phase transitions induced by temperature change are important. The U. S. and Korean PI's are highly respected scientists who, for several years, have been engaged in complimentary approaches to the solution of problems in the field of this proposal. This project is relevant to the objectives of the U.S.-Korea Cooperative Science Program which seeks to increase the level of cooperation between U.S. and Korean scientists and engineers through the exchange of scientific information, ideas, skills, and techniques and through collaboration on problems of mutual benefit.