The volume operator in covariant quantum gravity
arXiv:0911.0543 · doi:10.1088/0264-9381/27/16/165003
Abstract
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space.
10 pages. Version 2: proof extended to gamma > 1.
References in corpus (8)
- LQG vertex with finite Immirzi parameter
- A new spinfoam vertex for quantum gravity
- A New Spin Foam Model for 4d Gravity
- The loop-quantum-gravity vertex-amplitude
- Flipped spinfoam vertex and loop gravity
- Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
- Loop Quantum Cosmology and Spin Foams
- Coherent states, constraint classes, and area operators in the new spin-foam models
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- Complex Ashtekar variables and reality conditions for Holst's action
- Critical Overview of Loops and Foams
- Simple model for quantum general relativity from loop quantum gravity
- Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
- Branch-Cut Cosmology and the Bekenstein Criterion
- Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
- Spin foams
- Relating spin-foam to canonical loop quantum gravity by graphical calculus
- New insights in quantum geometry