Consistent Theory of Weak Interactions

In this paper we present an $S$-operator theory of weak interactions which fulfills all requirements of consistency, including unitarity. In an expansion to first order in $G$ the results are identical to those obtained in first-order perturbation theory from the standard Lagrangian formulation of weak interactions, but higher order corrections can be calculated. They are finite apart from a single infinite parameter which can be absorbed in a coupling-constant renormalization. It is shown that the renormalizations of the coupling constants in $\ensuremath{\mu}$ decay and $n$ decay are different. Higher order corrections to $e\ensuremath{-}{\ensuremath{\nu}}_{e}$ scattering are discussed. The complete renormalization of the theory is carried out. One of the main differences from standard Lagrangian theory is that the theory is not crossing symmetric.