Operators of quantum-reduced loop gravity from the perspective of full loop quantum gravity

Abstract: Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the quantum-reduced model from the perspective of full loop quantum gravity. We show that, in spite of their simplicity, the operators of the quantum-reduced model are simply the operators of the full theory acting on states in the Hilbert space of the quantum-reduced model. The passage from the full theory operators to the "reduced" operators simply consists of noting that the states of the quantum-reduced model are assumed to carry large spin quantum numbers, and discarding terms which are of lower than leading order in $j$. Our findings clarify the relation between the quantum-reduced model and full loop quantum gravity, and strengthen the technical foundations on which the kinematical structure of the quantum-reduced model is based.