Modelling Space with an Atom of Quantum Geometry

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 behavior of angles in three dimensional flat space require high-valence vertices with total spins of approximately 10^20.

18 pages, 11 figures

References in corpus (1)

• Operators for quantized directions

Cited by in corpus (15)

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• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Eigenvalues of the volume operator in loop quantum gravity
• Shape in an Atom of Space: Exploring quantum geometry phenomenology
• Quantum Geometry Phenomenology: Angle and Semiclassical States
• Linking shape dynamics and loop quantum gravity
• Properties of the Rovelli-Smolin-DePietri volume operator in the spaces of monochromatic intertwiners