Towards a Covariant Loop Quantum Gravity
arXiv:gr-qc/0608135
Abstract
We review the canonical analysis of the Palatini action without going to the time gauge as in the standard derivation of Loop Quantum Gravity. This allows to keep track of the Lorentz gauge symmetry and leads to a theory of Covariant Loop Quantum Gravity. This new formulation does not suffer from the Immirzi ambiguity, it has a continuous area spectrum and uses spin networks for the Lorentz group. Finally, its dynamics can easily be related to Barrett-Crane like spin foam models.
13 pages, review, draft chapter for the book "Approaches to quantum gravity", being prepared by Daniele Oriti for Cambridge University Press, comments welcome
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- Simplicity and closure constraints in spin foam models of gravity
- Critical Overview of Loops and Foams
- The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
- Plebanski Theory and Covariant Canonical Formulation
- Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
- Matter in Loop Quantum Gravity without time gauge: a non-minimally coupled scalar field
- In Search of Quantum de Sitter Space: Generalizing the Kodama State
- 3D Quantum Gravity from Holomorphic Blocks
- On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity