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This article concerns the problems regarding different lattice regularizationtechniques for the matter fields of Hamiltonian constraints defined in theframework of loop quantum gravity. The analysis is formulated in the phasespace-reduced cosmological model of the hypothetical theory of canonicalquantum general relativity. This article explains why a different thanlinks-related lattice smearing of fields leads to a local violation of generalcovariance. This happens by assuming, for instance, the nodes-related smearing.Therefore, this problem occurs in the case of any polymerlike scalar fieldquantization method by breaking the background independence of thesemiclassical predictions. In consequence, the diffeomorphism symmetry thatdepends on a links distribution is broken locally at the level of generallyrelativistic corrections. Moreover, by using the phase space-reduced gaugefixing technique to analyze this issue, the results are general and theyconcern any coupling with the links-regularized gravitational degrees offreedom in loop quantum gravity. Therefore, they lead to the following no-goconclusion. Any lattice smearing of matter, not defined by using thegeometrical distribution specified by the links-fluxes duality, violates thegeneral principle of relativity.

physical review. d/physical review. d.

Regularization of the cosmological sector of loop quantum gravity with  bosonic matter and the related problems with general covariance of quantum  corrections