Weak interactions and dispersion relations

The problem of including weak interactions in the Bogolyubov–Medvedev–Polivanov axiomatie approach is studied and one-dimensional dispersion relations are proved for elastic $\nu e$ scattering. The problem of deriving dispersion relations for weak interactions is considered in the framework of localizable axiomatic quantum theory, which was formulated earlier by the authors. In it, one permits a growth of the matrix elements in the momentum space off the mass shell which is slower than an arbitrary linear exponential, and it contains the ordinary axiomatie quantum theory of tempered growth as a special case.