Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-05-30
Physical Review D84 (2011) 104018
Physics
High Energy Physics
High Energy Physics - Theory
V1: 26 pages. V2: 28 pages. Several references added. Some references updated. Typos fixed. Minor changes in presentation. Thi
Scientific paper
10.1103/PhysRevD.84.104018
The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely though not exclusively by investigations of causal dynamical triangulations (CDT) and Horava gravity as possible candidates for quantum gravity. We advocate the use of the spectral dimension as a probe for the kinematics of these (and other) systems in the region where spacetime curvature is small, and the manifold is flat to a good approximation. In particular, we show how to assign a spectral dimension (as a function of so-called diffusion time) to any arbitrarily specified dispersion relation. We also analyze the fundamental properties of spectral dimension using extensions of the usual Seeley-DeWitt and Feynman expansions, and by saddle point techniques. The spectral dimension turns out to be a useful, robust and powerful probe, not only of geometry, but also of kinematics.
Sotiriou Thomas P.
Visser Matt
Weinfurtner Silke
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