  Gauge covariance properties of the scalar propagator in spinless/scalar
quantum electrodynamics (SQED) are explored in the light of the corresponding
Landau-Khalatnikov-Fradkin transformation (LKFT). These transformations are non
perturbative in nature and describe how each Green function of the gauge theory
changes under a variation of the gauge parameter. With a simple strategy,
considering the scalar propagator at the tree level in Landau gauge, we derive
a non perturbative expression for this propagator in an arbitrary covariant
gauge and three as well as four space-time dimensions. Some relevant
kinematical limits are discussed. Particularly, we compare our findings in the
weak coupling regime with the direct one-loop calculation of the said
propagator and observe perfect agreement up to an expected gauge independent
term. We further notice that some of the coefficients of the all-order
expansion for the propagator are fixed directly from the LKFT, a fact that
makes this set of transformations appealing over ordinary perturbative
calculations in gauge theories.
