Twistor Networks and Covariant Twisted Geometries

Etera R. Livine (1) , Simone Speziale (2) , Johannes Tambornino (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 CPT - Centre de Physique Théorique - UMR 6207

We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use this to define twistor networks as a graph carrying the phase space of two twistors on each edge. We also introduce simple twistor networks, which provide a classical version of the simple projected spin networks living on the boundary Hilbert space of EPRL/FK spin foam models. Finally, we give an expression for the Haar measure in terms of spinors.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

Etera R. Livine, Simone Speziale, Johannes Tambornino. Twistor Networks and Covariant Twisted Geometries. Physical Review D, 2012, 85 (6), pp.064002. ⟨10.1103/PhysRevD.85.064002⟩. ⟨hal-00644108⟩