The G_Newton --> 0 Limit of Euclidean Quantum Gravity

Details The G_Newton --> 0 Limit of Euclidean Quantum Gravity The G_Newton --> 0 Limit of Euclidean Quantum Gravity

1992-02-22

arxiv.org/abs/hep-th/9202076v1

Class.Quant.Grav.9:883-894,1992

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1088/0264-9381/9/4/007

Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an arbitrary anti-self-dual background. This theory is quantized in the loop representation and, as in the full theory, an infinite dimnensional space of exact solutions to the constraint is found. An inner product is also proposed. The path integral is constructed from the Hamiltonian theory and the measure is explicitly computed nonperturbatively, without relying on a semiclassical expansion. This theory could provide the starting point for a new approach to perturbation theory in $G_{Newton}$ that does not rely on a background field expansion and in which full diffeomorphism invariance is satisfied at each order.

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