Green's functions, states and renormalisation

The significance that is to be attached to different operator orderings of free quantum field theories in curved space-time is examined. It is hoped thus to elucidate the renormalization of such theories. It is argued that as in flat space, these theories should be rendered finite by normal ordering with respect to a local geometrical vacuum state. Flat space is considered first, then an analogous local, geometrical Green's function for curved space-time is defined. Examples given are the Einstein static universe, the open Einstein universe and the de Sitter universe. It is observed that normalization provides some insight into the nature of vacuum stress. (U.K.)