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:
Report number:
  • AEI-2014-028

Citations per year

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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<α
Note:
  • 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