de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Discrete quantum geometries and their effective dimension

Thürigen, J. (2015). Discrete quantum geometries and their effective dimension. PhD Thesis.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0028-FE72-8 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-3BC4-C
Genre: Thesis

Files

show Files
hide Files
:
1510.08706.pdf (Preprint), 3MB
Description:
File downloaded from arXiv at 2015-11-11 11:50
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-

Locators

show

Creators

show
hide
 Creators:
Thürigen, Johannes1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

Content

show
hide
Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th, Physics, History of Physics, physics.hist-ph
 Abstract: In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension $d$ on low energy scales to a real number $0<\alpha<d$ on high energy scales. In the particular case of $\alpha=1$ these results allow to understand the quantum geometry as effectively fractal.

Details

show
hide
Language(s):
 Dates: 2015-10-2920152015
 Publication Status: Published in print
 Pages: PhD thesis, Humboldt-Universit\"at zu Berlin; urn:nbn:de:kobv:11-100232371; http://edoc.hu-berlin.de/docviews/abstract.php?id=42042
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Degree: PhD

Event

show

Legal Case

show

Project information

show

Source

show