Weak Interaction Effects in Electrodynamics

Abstract

A perturbation calculation with cutoff is performed for electron scattering in an external electromagnetic field to lowest order in the weak interactions, assuming an intermediate vector meson. Renormalization is based on recent general results of Sekine in a theory with a parity nonconserving interaction. The renormalized $S$ matrix is then used to obtain a close estimate of the parity impurities present in atomic and molecular states due to the weak interactions of the electrons. In particular the $2^{2}P$ admixture to the $2^{2}S$ state of hydrogen is found to be about ${10}^{\ensuremath{-}12}$ for reasonable values of the parameters. The calculation agrees with general considerations on electromagnetic properties of leptons advanced by Zel'dovich and Perelomov, but yields an estimate of the hydrogen amplitude smaller by ${10}^{\ensuremath{-}3}$. A theoretical upper limit of ${10}^{\ensuremath{-}18}$ on the parity impurity of the ground state of ${\mathrm{O}}_{2}$ is suggested, well below the experimental upper limit of 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$.