  We find that, in the local V-A theory, the radiative corrections to pion
beta-decay involving the weak vector current, when evaluated in the current
algebra (CA) formulation in which quarks are the fundamental underlying fields,
show a small difference with the more elementary calculations based directly on
the pion fields. We show that this difference arises from a specific
short-distance effect that depends on the algebra satisfied by the weak and
electromagnetic currents. On the other hand, we present a simple theoretical
argument that concludes that this difference does not occur when the CA
formulation is compared with the chiral perturbation theory (chiPT) approach.
Comparisons with previous studies, and with a more recent calculation based on
chiPT, are included. We also briefly review the important differences between
the results in the local V-A theory and the Standard Model.
