Poincare 2-group and quantum gravity

Details Poincare 2-group and quantum gravity Poincare 2-group and quantum gravity

2011-10-21

arxiv.org/abs/1110.4694v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

v2: sections 4 and 5 substantially modified, new results and one reference added

Scientific paper

We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge lengths of the spacetime manifold triangulation arise as the basic variables in the path-integral quantization, while the state-sum amplitude is an evaluation of a colored 3-complex, in agreement with the category theory results. A 3-complex amplitude for Euclidean quantum gravity is proposed.

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