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The century of the incomplete revolution: searching for general relativistic quantum field theory
Carlo Rovelli
In fundamental physics, this has been the century of quantum mechanics and general relativity. It has also been the century of the long search for a conceptual framework capable of…
Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
R. De Pietri, L. Freidel, K. Krasnov +1
Boulatov and Ooguri have generalized the matrix models of 2d quantum gravity to 3d and 4d, in the form of field theories over group manifolds. We show that the Barrett-Crane quantu…
Refined Algebraic Quantization in the oscillator representation of SL(2,R)
Jorma Louko, Carlo Rovelli
We investigate Refined Algebraic Quantization (RAQ) with group averaging in a constrained Hamiltonian system with unreduced phase space T^*R^4 and gauge group SL(2,R). The reduced…
Spectral noncommutative geometry and quantization: a simple example
Carlo Rovelli
We explore the relation between noncommutative geometry, in the spectral triple formulation, and quantum mechanics. To this aim, we consider a dynamical theory of a noncommutative…
SL(2,R) model with two Hamiltonian constraints
Merced Montesinos, Carlo Rovelli, Thomas Thiemann
We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity,…