Weak Interactions at High Energies

We discuss the weak interactions from an $S$-matrix point of view in order to make some qualitative statements about high-energy behavior. In order to separate the weak interactions from others as much as possible, attention is focused on the weak interactions of leptons neglecting electromagnetism. We examine the consequences of imposing the constraints of unitarity and analyticity on weak amplitudes whose low-energy behavior is assumed to be correctly given by the usual Fermi theory (including the possibility of neutral currents). We first study corrections to the low-energy limit by using the Mandelstam iteration to express all lepton-lepton two-body scattering amplitudes to third order in the Fermi constant in terms of a small number of subtraction constants. We then speculate beyond perturbation theory. We discuss some consequences of forward dispersion relations and propose a mechanism for providing the necessary damping of weak amplitudes at high energies. The mechanism is the existence of the intermediate vector boson coupled weakly to leptons but interacting strongly with itself. We examine some consequences of this hypothesis.