de.mpg.escidoc.pubman.appbase.FacesBean
Deutsch
 
Hilfe Wegweiser Datenschutzhinweis Impressum Kontakt
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT
  Discrete quantum geometries and their effective dimension

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

Item is

Basisdaten

einblenden: ausblenden:
Datensatz-Permalink: http://hdl.handle.net/11858/00-001M-0000-0028-FE72-8 Versions-Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-3BC4-C
Genre: Hochschulschrift

Dateien

einblenden: Dateien
ausblenden: Dateien
:
1510.08706.pdf (Preprint), 3MB
Beschreibung:
File downloaded from arXiv at 2015-11-11 11:50
Sichtbarkeit:
Öffentlich
MIME-Typ / Prüfsumme:
application/pdf / [MD5]
Technische Metadaten:
Copyright Datum:
-
Copyright Info:
-

Externe Referenzen

einblenden:

Urheber

einblenden:
ausblenden:
 Urheber:
Thürigen, Johannes1, Autor              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

Inhalt

einblenden:
ausblenden:
Schlagwörter: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th, Physics, History of Physics, physics.hist-ph
 Zusammenfassung: 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

einblenden:
ausblenden:
Sprache(n):
 Datum: 2015-10-2920152015
 Publikationsstatus: Im Druck publiziert
 Seiten: PhD thesis, Humboldt-Universit\"at zu Berlin; urn:nbn:de:kobv:11-100232371; http://edoc.hu-berlin.de/docviews/abstract.php?id=42042
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Art des Abschluß: Doktorarbeit

Veranstaltung

einblenden:

Entscheidung

einblenden:

Projektinformation

einblenden:

Quelle

einblenden: