Quantum fields in curved spaces: Kinetic theory

The extension of flat space quantum kinetic theory to curved space-times is described. This is accomplished by implementing a generalized Wigner transformation on the Hadamard function of the field theory. A quasilocal momentum space is introduced via Riemann normal coordinates. An exact treatment of the field in purely kinetic terms is impossible; off-shell behavior is accounted for, to some degree, by the introduction of an expansion around the mass-shell. In curved spacetime, free scalar and spinor fields are considered. It is shown that the Wigner transformation leads to quantum corrected Einstein-Vlasov equations having the expected classical limits. The stress tensor for a free scalar field is constructed in terms of the Wigner function. Divergences are isolated by dimensional regularization and covariant conservation is demonstrated. A model of time-dependent oscillators is considered. The oscillators have time dependent frequencies and interactions. An exact Langevin equation for the system is derived. The model is then studied in a settling appropriate for de Sitter space. Two new effects are found: (1) a time dependent contribution to the effective potential with indeterminate sign and (2) a noise-dependent viscosity