  This article concerns the problems regarding different lattice regularization
techniques for the matter fields of Hamiltonian constraints defined in the
framework of loop quantum gravity. The analysis is formulated in the phase
space-reduced cosmological model of the hypothetical theory of canonical
quantum general relativity. This article explains why a different than
links-related lattice smearing of fields leads to a local violation of general
covariance. This happens by assuming, for instance, the nodes-related smearing.
Therefore, this problem occurs in the case of any polymerlike scalar field
quantization method by breaking the background independence of the
semiclassical predictions. In consequence, the diffeomorphism symmetry that
depends on a links distribution is broken locally at the level of generally
relativistic corrections. Moreover, by using the phase space-reduced gauge
fixing technique to analyze this issue, the results are general and they
concern any coupling with the links-regularized gravitational degrees of
freedom in loop quantum gravity. Therefore, they lead to the following no-go
conclusion. Any lattice smearing of matter, not defined by using the
geometrical distribution specified by the links-fluxes duality, violates the
general principle of relativity.
