Electromagnetic Corrections, Current Algebra, and the Intermediate Boson

Assuming that the weak interactions are mediated by vector bosons, it is shown that the divergent parts of the second-order electromagnetic corrections to $\mu$ and $\beta$ decays are identical in the limit of zero momentum transfer to the leptons. Therefore, in such a case the corrections to $\frac{G_V}{G_{\mu }}$ are finite. Implications of this result for the space-space part of the current algebra are briefly discussed.