Algebraic approach to quantum gravity III: noncommmutative Riemannian geometry

Details Algebraic approach to quantum gravity III: noncommmutative Riemannian geometry Algebraic approach to quantum gravity III: noncommmutative Riemannian geometry

2006-04-19

arxiv.org/abs/hep-th/0604132v1

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 1 .eps figure, to appear in collection B. Fauser and J. Tolksdorf, eds., Birkhauser

Scientific paper

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that arises naturally as the classical limit; a theory with nonsymmetric metric and a skew version of metric compatibilty. Meanwhile, in quantum gravity a key ingredient of our approach is the proposal that the differential structure of spacetime is something that itself must be summed over or `quantised' as a physical degree of freedom. We illustrate such a scheme for quantum gravity on small finite sets.

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