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We focus on three-dimensional QRLG with the purpose of shedding light on thelink between reduced LQG and LQC in four space-time dimensions. Consideringhomogeneous three-dimensional LQG, the theory simplifies to QRLG. We thenimplement Thiemann's Quantum Spin Dynamics for Euclidean three-dimensionalspace-time in presence of a real scalar matter field. We deploy a polymerquantization of the scalar field while using methods of quantum reduced loopgravity. We compute the scalar Hamiltonian operator on the states of thekinematical Hilbert space of the theory, and exhibit its matrix elements thatare derived using a new simplified method. The coupling to matter, which playsthe role of a carrier of dynamics, opens the pathway to the study ofphenomenological implications. We finally comment on the relations betweenthree-dimensional QRLG and LQC, as well as on the appearance of thecorrespondence principle for the scalar field.

2+1 homogeneous Loop Quantum Gravity with a scalar field clock