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Quantum Fields in Curved Space N. D. Birrell, P. C. W. Davies
Publisher: Cambridge University Press

Jacobson Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect - 2004). Topics discussed here include: a comparison with Euclidean quantum field theory, supersymmetry and general relativity. If it is a graviton field then it is not the curvature of space-time but the interaction of the graviton force particles. 'Sketchy', in my own sense that some approximations have to be made in the classical solutions of the field equations in the background of a curved space-time and bring these over to the context of a quantum field theory. Us that “facts” are very fluid in nature and “verification” is a matter of recordable duplication of observable phenmomena (see: T. Or indeed the Quantum Field, Higgs Field, New Luminiferous Ether, or whatever else we may end up calling it. Well, the issue is that professor Wisdom's 'breaststroke' is not particularly effective to overcome earth's gravity, as it relies on the local curvature of spacetime. The fancy new piece of machinery (by then an old hat for string theorists and a really old hat for relativists) was the spin connection which allows us to connect the flat-space formalism for spinors to curved spaces. In 1997, Juan Maldacena made the startling conjecture that theories of gravity on curved spaces are equivalent to ordinary quantum field theories confined to the boundaries of those spaces. For more information about the spin connection in the language of quantum field theory, Bertlemann's “Anomalies in Quantum Field Theory” seems very comprehensive. If gravity is the curvature of space-time then how can it ever be described by a quantum theory. This curvature is very small, and its effects are hardly noticable in everyday life and over small distances. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, University of Chicago Press 1994; The back reaction effect in particle creation in curved spacetime, Commun. First to show how to place fermion fields in the bulk.