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Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limitof Euclidean or complexified general relativity is not a free field theory, butis a theory that describes a linearized self-dual connection propagating on anarbitrary anti-self-dual background. This theory is quantized in the looprepresentation and, as in the full theory, an infinite dimnensional space ofexact solutions to the constraint is found. An inner product is also proposed.The path integral is constructed from the Hamiltonian theory and the measure isexplicitly computed nonperturbatively, without relying on a semiclassicalexpansion. This theory could provide the starting point for a new approach toperturbation theory in $G_{Newton}$ that does not rely on a background fieldexpansion and in which full diffeomorphism invariance is satisfied at eachorder.Comment: 14 page

The G Newton to 0 limit of Euclidean quantum gravity

The G _Newton to 0 limit of Euclidean quantum gravity