Long-Range Corrections to the Coulomb Potential and Their Implications about Weak Interactions

We calculate corrections to the photon propagator due to the creation of virtual neutrino pairs. These are shown to result in long-range ($\frac{1}{r^3}$- and $\frac{1}{r^5}$-type) corrections to the Coulomb potential. It is shown that these corrections are of significance because upper limits on their strengths lead to upper limits on the weak interaction cutoff $\Lambda$, and on possible nonconservation of the "$\mu$ quantum number." A discussion is given of these upper limits as obtained from the present accuracy of Lamb-shift measurements.