The theta parameter in loop quantum gravity: effects on quantum geometry and black hole entropy

Abstract

The precise analog of the theta-quantization ambiguity of Yang-Mills theory exists for the real SU(2) connection formulation of general relativity. As in the former case theta labels representations of large gauge transformations, which are super-selection sectors in loop quantum gravity. We show that unless theta=0, the (kinematical) geometric operators such as area and volume are not well defined on spin network states. More precisely the intersection of their domain with the dense set Cyl in the kinematical Hilbert space H of loop quantum gravity is empty. The absence of a well defined notion of area operator acting on spin network states seems at first in conflict with the expected finite black hole entropy. However, we show that the black hole (isolated) horizon area--which in contrast to kinematical area is a (Dirac) physical observable--is indeed well defined, and quantized so that the black hole entropy is proportional to the area. The effect of theta is negligible in the semiclassical limit where proportionality to area holds.

References in corpus (17)

• Background Independent Quantum Gravity: A Status Report
• Quantum Geometry and Black Hole Entropy
• Quantum Spin Dynamics (QSD)
• Black hole entropy in Loop Quantum Gravity
• Black Hole Entropy from Loop Quantum Gravity
• Black hole entropy from Quantum Geometry
• Isolated Horizons: Hamiltonian Evolution and the First Law
• Reality conditions inducing transforms for quantum gauge field theory and quantum gravity
• Non-minimally coupled scalar fields and isolated horizons
• A Real Polynomial Formulation of General Relativity in terms of Connections
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• The Chern-Simons Invariant as the Natural Time Variable for Classical and Quantum Cosmology
• Yang-Mills analogues of the Immirzi ambiguity
• Non-minimal couplings, quantum geometry and black hole entropy
• The linearization of the Kodama state
• Self-dual gravity with topological terms
• Is the Exponential of the Chern-Simons Action a Normalizable Physical State?

Cited by in corpus (6)

• Black Holes in Loop Quantum Gravity
• 4d Lorentzian Holst action with topological terms
• Quantum gravity kinematics from extended TQFTs
• Actions, topological terms and boundaries in first order gravity: A review
• Hamiltonian and Noether charges in first order gravity
• Some notes on the Kodama state, maximal symmetry, and the isolated horizon boundary condition