Infrared divergences, the renormalization group and vertex functions at inhomogeneous momentum scales

The renormalization group of a Φ4 theory in four dimensions is interpreted and extended to enable a meaningful calculation of vertex functions in the perturbative regions where the momentum scales are very uneven. Specific techniques are developed for the propagator, four-point function and higher-order vertex functions. Infrared divergences are identified as the consequence of an inadequate treatment of inhomogeneous momentum scales: They no longer appear when the mentioned techniques are applied. It is expected that an analogous development can be carried out in other infrared free-field theories. (orig.)