Quantum Gravity Hamiltonian for Manifolds with Boundary

Abstract

In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open Wilson lines in the new variables formulation of quantum gravity. In cases where the boundary conditions fix the metric on the boundary (e.g., in the asymptotically Minkowskian case) one can obtain a finite result, given by a `shift operator' generating translations of the Wilson line in the direction of its tangent vector. A similar shift operator serves as the Hamiltonian constraint in Morales-Técotl and Rovelli's work on quantum gravity coupled to Weyl spinors. This suggests the appearance of an induced field theory of Weyl spinors on the boundary, analogous to that considered in Carlip's work on the statistical mechanics of the 2+1-dimensional black hole.

17 pages in LaTeX format, vastly improved version

References in corpus (9)

• Discreteness of area and volume in quantum gravity
• The Gravitational Hamiltonian, Action, Entropy, and Surface Terms
• The Statistical Mechanics of the (2+1)-Dimensional Black Hole
• Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
• Edge states in Gravity and Black Hole Physics
• Fermions in Quantum Gravity
• Knots and Quantum Gravity: Progress and Prospects
• Mathematical Problems of Non-perturbative Quantum General Relativity
• Regularization of the Hamiltonian constraint and the closure of the constraint algebra

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• Open-Flux Solutions to the Constraints for Plane Gravity Waves
• The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity
• Boundary States and Black Hole Entropy