A broad class of transport processes in matter at high densities and temperatures will be studied. One of the main objectives of this theoretical physics research will be to study the role played by weakly interacting particles under astrophysical settings in order to obtain clues to the properties of these particles. The specific questions to be addressed are as follows: What are the effects of such particles on stellar evolution, especially when they are produced thermally and contribute as an energy loss mechanism? Can one obtain any constraints on these particles from observational data of stellar evolution? In additional work, the properties of relativistic shock waves in which electron- positron pairs are produced in the post-shock matter, astrophysical plasmas, quark matter, and positron transport will be studied. The outcome of these studies is expected to elucidate the new interactions in particle physics and to contribute to a better understanding of matter under extreme conditions in many-body physics. The results will have a direct bearing on observational astronomy at radio to X-ray and gamma-ray wavelengths.