Maité Dupuis

Holomorphic Lorentzian simplicity constraints

We develop a 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 space-like 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.

Observables in Loop Quantum Gravity with a cosmological constant

An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant

Discrete Gravity Models and Loop Quantum Gravity: a Short Review ?

\Lambda

Towards the Turaev-Viro amplitudes from a Hamiltonian constraint

. In 3d, Chern-Simons theory provides some guiding lines:

Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models

\Lambda

Deformed spinor networks for loop gravity: towards hyperbolic twisted geometries

appears in the quantum deformation of the gauge group. The Turaev-Viro model, which is an example of spin foam model is also defined in terms of a quantum group. By extension, it is believed that in 4d, a quantum group structure could encode the presence of

Spinors group field theory and Voros star product: First contact

\Lambda\neq0

Quantum hyperbolic geometry in loop quantum gravity with cosmological constant

. In this article, we introduce by hand the quantum group

Discretization of 3d gravity in different polarizations

\mathcal{U}_{q}(\mathfrak{su}(2))

Deformed phase space for 3d loop gravity and hyperbolic discrete geometries

into the LQG framework, that is we deal with