Anomalous dimension in semiclassical gravity

Details Anomalous dimension in semiclassical gravity Anomalous dimension in semiclassical gravity

2011-08-06

arxiv.org/abs/1108.1507v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTeX, 9 pages, 1 figure; v2: typos corrected and reference added

Scientific paper

The description of the phase space of relativistic particles coupled to three-dimensional Einstein gravity requires momenta which are coordinates on a group manifold rather than on ordinary Minkowski space. The corresponding field theory turns out to be a non-commutative field theory on configuration space and a group field theory on momentum space. Using basic non-commutative Fourier transform tools we introduce the notion of non-commutative heat-kernel associated with the Laplacian on the non-commutative configuration space. We show that the spectral dimension associated to the non-commutative heat kernel varies with the scale reaching a non-integer value smaller than three for Planckian diffusion scales.

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