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Nowadays projective quantum states can be constructed for a number of fieldtheories including Loop Quantum Gravity. However, these states are kinematic inthis sense that their construction does not take into account the dynamics ofthe theories. In particular, the construction neglects constraints on phasespaces. Here we present projective quantum states for a "toy-theory" calleddegenerate Plebanski gravity which satisfy a constraint of this theory.

Constrained projective quantum states for the degenerate Plebanski gravity