Quantum Field Theory on Curved Backgrounds

Abstract

We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally covariant classical field theory. For all that, methods from microlocal analysis combined with some methods from global analysis, namely differentiation on locally convex spaces, and category theory are crucially employed.

19 pages, submitted for the Proceedings of the Kompaktkurs "Quantenfeldtheorie auf gekruemmten Raumzeiten" held at Universitaet Potsdam, Germany, in 8.-12.10.2007, organized by C. Baer and K. Fredenhagen