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Classical and Quantum Gravity on Conformal Superspace

Julian Barbour·Niall O Murchadha
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Abstract

The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of a four-dimensional gauge group of arbitrary coordinate and conformal transformations of riemannian metrics defined on a three-manifold. This new symmetry is more restrictive and hence more predictive. Many of the difficulties that have plagued the canonical quantization of general relativity seem to vanish.

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Julian Barbour, Niall O Murchadha. 1999-11-19. Classical and Quantum Gravity on Conformal Superspace. https://arxiv.org/abs/gr-qc/9911071

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