Holomorphic Lorentzian Simplicity Constraints - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Physics Année : 2012

Holomorphic Lorentzian Simplicity Constraints

Résumé

We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including gl(N,C) as a subalgebra. Then, we define the linear and quadratic simplicity constraints which reduce the spinor variables to (framed) 3d spacelike polyhedra embedded in Minkowski spacetime. Finally, we introduce a new version of the simplicity constraints which (i) are holomorphic and (ii) Poisson-commute with each other, and show their equivalence to the linear and quadratic constraints.

Dates et versions

hal-00611822 , version 1 (27-07-2011)

Identifiants

Citer

Maité Dupuis, Laurent Freidel, Etera R. Livine, Simone Speziale. Holomorphic Lorentzian Simplicity Constraints. Journal of Mathematical Physics, 2012, 53, pp.032502. ⟨10.1063/1.3692327⟩. ⟨hal-00611822⟩
140 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More