On the role of the Barbero-Immirzi parameter in discrete quantum gravity

Abstract

The 1-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them Loop Quantum Gravity and Spin Foams. It facilitates the loop quantization programme and subsequently the Barbero-Immirzi parameter (gamma) arises in both the spectra of geometrical operators and in the dynamics provided by Spin Foams. However, the debate continues as to whether quantum physics should be Barbero-Immirzi parameter dependent. Starting from a discrete SO(4)-BF theory phase space, we find two possible reductions with respect to a discrete form of the simplicity constraints. The first reduces to a phase space with gamma-dependent symplectic structure and more generally in agreement with the phase space underlying Loop Quantum Gravity restricted to a single graph - a.k.a. Twisted Geometries. The second, fuller reduction leads to a gamma-independent symplectic structure on the phase space of piecewise-flat-linear geometries - a.k.a. Regge geometries. Thus, the gamma-dependence of physical predictions is related to the choice of phase space underlying the quantization.

16 + 12 pages

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• Quantum group spin nets: refinement limit and relation to spin foams
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Discrete gravity dynamics from effective spin foams
• Discretization independence implies non-locality in 4D discrete quantum gravity
• The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
• Dirac's discrete hypersurface deformation algebras
• The spin connection of twisted geometry
• A note on the Holst action, the time gauge, and the Barbero-Immirzi parameter
• Spinning geometry = Twisted geometry
• From spin foams to area metric dynamics to gravitons
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• Quantum geometry from higher gauge theory
• Hamiltonian spinfoam gravity
• Lorentzian quantum cosmology from effective spin foams
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• Area-metric gravity revisited
• The thermodynamics of isolated horizons in loop quantum gravity
• Towards self dual Loop Quantum Gravity
• Modified Graviton Dynamics From Spin Foams: The Area Regge Action
• From area metric backgrounds to the cosmological constant and corrections to the Polyakov action
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• Simplicity constraints: a 3d toy-model for Loop Quantum Gravity