Modelling space with an atom of quantum geometry

Type of Work

Article

Date

2002

Journal Title

Classical and Quantum Gravity

Journal ISSN

0264-9381

Journal Volume

19

Journal Issue

8

First Page

2211

Last Page

2228

DOI

10.1088/0264-9381/19/8/311

Abstract

Within the context of loop quantum gravity there are several operators which measure geometry quantities. This work examines two of these operators, volume and angle, to study quantum geometry at a single spin network vertex—'an atom of geometry'. Several aspects of the angle operator are examined in detail including minimum angles, level spacing and the distribution of angles. The high spin limit of the volume operator is also studied for monochromatic vertices. The results show that demands of the correct scaling relations between area and volume and requirements of the expected behaviour of angles in three-dimensional flat space require high-valence vertices with total spins of approximately 1020.

Hamilton Areas of Study

Physics

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