Spinors and Twistors in Loop Gravity and Spin Foams
arXiv:1201.2120
Abstract
Spinorial tools have recently come back to fashion in loop gravity and spin foams. They provide an elegant tool relating the standard holonomy-flux algebra to the twisted geometry picture of the classical phase space on a fixed graph, and to twistors. In these lectures we provide a brief and technical introduction to the formalism and some of its applications.
16 pages; to appear in the Proceedings of the 3rd Quantum Gravity and Quantum Geometry School, February 28 - March 13, 2011 Zakopane, Poland. v2: minor amendments
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Cited by in corpus (15)
- Observables in Loop Quantum Gravity with a cosmological constant
- The twistorial structure of loop-gravity transition amplitudes
- Discrete Gravity Models and Loop Quantum Gravity: a Short Review
- Pachner moves in a 4d Riemannian holomorphic Spin Foam model
- Linking covariant and canonical LQG II: Spin foam projector
- Intertwiner Entanglement on Spin Networks
- Quantum hyperbolic geometry in loop quantum gravity with cosmological constant
- Holonomy Operator and Quantization Ambiguities on Spinor Space
- Bulk amplitude and degree of divergence in 4d spin foams
- The Construction of Spin Foam Vertex Amplitudes
- Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a Cut-off for Quantum Gravity
- Classical dynamics for Loop Gravity: The 2-vertex model
- A one-dimensional action for simplicial gravity in three dimensions
- Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations
- A simpler way of imposing simplicity constraints