Fröhlich  has advocated the need for a proof of reflection positivity of the Regge path integral, which one may expect to play a role in proving the unitarity of the theory. This can be formulated as a condition on the path-integral measure (including the action) under the gluing of two simplicial four-manifolds along a three-dimensional boundary.
Other authors have suggested associating gauge-theoretic instead of metric variables with the building blocks of a simplicial complex, for the case of the Poincaré group , the Lorentz group , and for Ashtekar gravity with gauge group [131, 132], and reformulating the quantum theory in terms of them.
Hamiltonian 3+1 versions of Regge calculus have been studied classically (see  for a review), but attempts to quantize them have not progressed very far. One meets problems with the definition of the constraints and the (non-)closure of their Poisson algebra. A recent proposal for constructing a canonical quantum theory is due to Mäkelä , who constructed a simplicial version of the Wheeler–DeWitt equation, based on the use of area instead of length variables (which however are known to be overcomplete). In a similar vein, Khatsymovsky  has suggested that the operators measuring spatial areas ought to have a discrete spectrum.
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