The G_Newton --> 0 Limit of Euclidean Quantum Gravity

TL;DR

This paper investigates the G_{Newton} --> 0 limit of Euclidean quantum gravity using Ashtekar variables, revealing it as a linearized self-dual connection theory on anti-self-dual backgrounds, with a nonperturbative quantization approach.

Contribution

It introduces a novel nonperturbative quantization of the G_{Newton} --> 0 limit, providing a background-independent perturbation framework in Euclidean quantum gravity.

Findings

The G_{Newton} --> 0 limit is a linearized self-dual connection theory.

An infinite-dimensional space of solutions to the constraints is identified.

A nonperturbative path integral measure is explicitly constructed.

Abstract

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.