Quantum-reduced loop gravity from a master constraint (Ilkka Mäkinen, National Centre for Nuclear Physics, Warsaw)

We construct a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which fix the densitized triad to be diagonal. We establish a set of solutions of the constraint operator and study the action of the basic operators of loop quantum gravity on these states. If the resulting expressions are truncated at leading order in the spin quantum number, we recover the kinematical framework of quantum-reduced loop gravity, a model proposed by Alesci and Cianfrani as an attempt to probe the physical content of loop quantum gravity.