  The use of lattice tensor representations is explored to investigate the
lattice Landau gauge gluon propagator for the pure SU(3) Yang-Mills gauge
theory in 4D. The analysis of several tensor bases allows to quantify the
completeness of the various tensor bases considered, the deviations of the
lattice results from the continuum theory due to the lattice artefacts and
estimate the theoretical uncertainty in the propagator. Furthermore, our
analysis tests continuum based relations with the lattice data and show that
the lattice Landau gauge gluon propagator is described by a unique form factor,
as in the continuum formulation.
