Instanton representation of Plebanski gravity XX. Minisuperspace   quantization of gravity coupled to the Klein--Gordon scalar field
  In this paper we quantize the Klein--Gordon scalar field coupled to gravity in the instanton representation for spatially homogeneous variables. The construction provides a well-defined Hilbert space of states for generic self-interaction potential V, with a direct link to the semiclassical limit below the Planck scale. Additionally, we compute the Hamilton's equations of motion for this model, performing various consistency checks on the quantum theory. 
Eyo Eyo Ita III