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New spinfoam vertex for quantum gravity
We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the
Polyhedra in loop quantum gravity
Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a
Twisted geometries: A geometric parametrisation of SU(2) phase space
A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this
Area?angle variables for general relativity
We introduce a modified Regge calculus for general relativity on a triangulated four-dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These
Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the coherent state techniques introduced earlier
SU(2) graph invariants, Regge actions and polytopes
We revisit the the large spin asymptotics of 15j symbols in terms of cosines of the 4d Euclidean Regge action, as derived by Barrett and collaborators using a saddle point approximation. We bring it
Twistors to twisted geometries
In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic
Reconcile Planck scale discreteness and the Lorentz-Fitzgerald contraction
A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted
Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
The Lorentzian EPRL spin foam amplitude for loop quantum gravity is a multi-dimensional non-compact integral of highly oscillating functions. Using a method based on the decomposition of