Holomorphic Lorentzian Simplicity Constraints
General Relativity and Quantum Cosmology
2015-05-28 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1107.5274,
title = {Holomorphic Lorentzian Simplicity Constraints},
author = {Maité Dupuis and Laurent Freidel and Etera R. Livine and Simone Speziale},
journal= {arXiv preprint arXiv:1107.5274},
year = {2015}
}
Comments
20 pages. v2: explicit counting of the holomorphic constraints added, and minor amendments