Anomalous dimension in semiclassical gravity
Abstract
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.
Cite
@article{arxiv.1108.1507,
title = {Anomalous dimension in semiclassical gravity},
author = {Emanuele Alesci and Michele Arzano},
journal= {arXiv preprint arXiv:1108.1507},
year = {2015}
}
Comments
RevTeX, 9 pages, 1 figure; v2: typos corrected and reference added