Analysis of interacting quantum field theory in curved space-time

A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given. Reduction formulas for S-matrix elements in terms of vacuum Green’s functions are derived, special attention being paid to the possibility that the ’’in’’ and ’’out’’ vacuum states may not be equivalent. Green’s functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for λφ3(4,6) field theories. The extension of these techniques to curved spacetimes is considered. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, φ3(4) is proven renormalizable in a large class of spacetimes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes.