On How the Scalar Propagator Transforms Covariantly in Spinless Quantum Electrodynamics

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.