Dimensional flow in discrete quantum geometries
Dec 29, 2014
11 pages
Published in:
- Phys.Rev.D 91 (2015) 8, 084047
- Published: Apr 20, 2015
e-Print:
- 1412.8390 [hep-th]
Report number:
- AEI-2014-028
View in:
Citations per year
Abstract: (APS)
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension d at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number 0<αNote:
- 11 pages, 6 figures. v2: discussion improved at several points, typos corrected, results and conclusions unchanged
- 04.60.-m
- 04.60.Pp
- quantum geometry
- quantum gravity: loop space
- dimension: spectral
- flow
- fractal
References(49)
Figures(6)
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