Coherent State Operators in Loop Quantum Gravity

Abstract

We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function on a classical phase space. Using the heat kernel coherent states of Hall and Thiemann, we show how to construct operators corresponding to functions depending on holonomies and fluxes associated to a fixed graph. We construct the coherent state versions of the fundamental holonomy and flux operators, as well as the basic geometric operators of area, angle and volume. Our calculations show that the corresponding canonical operators are recovered from the coherent state operators in the limit of large spins.

34 pages, 4 figures (plus many pretty diagrams)

References in corpus (7)

• A new spinfoam vertex for quantum gravity
• Polyhedra in loop quantum gravity
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
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Cited by in corpus (5)

• Twisted Geometries Coherent States for Loop Quantum Gravity
• Loop Quantum Gravity's Boundary Maps
• Conformal loop quantum gravity coupled to the Standard Model
• On the polymer quantization of connection theories: graph coherent states
• Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners