Analyticity of effective coupling and propagators in massless models of quantum field theory

For massless models of quantum field theory, some general theorems are proved concerning the analytic continuation of the renormalization group functions as well as the effective coupling and the propagators. Starting points are analytic properties of the effective coupling and the propagators in the momentum variable k2, which can be converted into analyticity of β- and γ-functions in the coupling parameter lambda. It is shown that the β-function can have branch point singularities related to stationary points of the effective coupling as a function of k2. The type of these singularities of β(lambda) can be determined explicitly. Examples of possible physical interest are extremal values of the effective coupling at space-like points in the momentum variable, as well as complex conjugate stationary points close to the real k2-axis. The latter may be related to the sudden transition between weak and strong coupling regimes of the system. Finally, for the effective coupling and for the propagators, the analytic continuation in both variables k2 and lambda is discussed. (orig.)