  In this work we show how to construct the one-loop vacuum polarization for
light-front QED$_{4}$ in the framework of the perturbative causal theory.
Usually, in the canonical approach, it is considered for the fermionic
propagator the so-called instantaneous term, but it is known in literature that
this term is controversial because it can be omitted by computational reasons;
for instance, by compensation or vanishing by dimensional regularization. In
this work we propose a solution to this paradox. First, in the perturbative
causal theory, it is shown that the fermionic propagator does not have
instantaneous terms, and with this propagator we calculate the one-loop vacuum
polarization, from the calculation it follows the same result as obtained by
the standard approach, but without reclaiming any extra assumptions. Moreover,
since the perturbative causal theory is defined in the distributional
framework, we can also show the reason behind we obtaining the same result
whether we consider or not the instantaneous fermionic propagator term.
