ANALYTIC PERTURBATION-THEORY IN QCD AND SCHWINGERS CONNECTION BETWEENTHE BETA-FUNCTION AND THE SPECTRAL DENSITY

We argue that a technique called analytic perturbation theory leads to a well-defined method for analytically continuing the running couplin g constant from the spacelike to the timelike region, which allows us to give a self-consistent definition of the running coupling constant for timelike momentum. The corresponding beta function is proportional to the spectral density, which confirms a hypothesis due to Schwinger .