Applications of Current Commutation Relations to Muon Capture and Neutrino (Antineutrino) Reactions in Nuclei

Relations among total muon-capture rates in nuclei and the equal-time commutators of the space and time components of the strangeness-conserving weak hadron current are derived. Using the quark field algebra and the closure approximation, this relation yields a total muon-capture rate in ${\mathrm{He}}^3$ of $\Gamma \left({\mathrm{He}}^3\right)\approx 2.36\times {10}^3$ ${\sec }^{-1\mathrm{}}$, in very good agreement with experiment. We demonstrate that application of the gauge field algebra to our relations does not yield a result that can be compared with experiment, since we cannot justify the use of the closure approximation in the context of this algebra. Using the quark field algebra and the closure approximation, similar relations are also derived for the total "elastic" differential cross section for forward scattering of neutrinos off nuclei.