Finite calculation of divergent self-energy diagrams

Abstract

Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important features of such dispersive techniques in the framework of the so-called finite causal perturbation theory. The method is also applied to the "divergent" general massive two-loop sunrise self-energy diagram, where it leads directly to an analytic expression for the imaginary part of the diagram in accordance with the literature, whereas the real part can be obtained by a single integral dispersion relation. It is pointed out that dispersive methods have been known for decades and have been applied to several nontrivial Feynman diagram calculations.PACS Nos.: 11.10.–z, 11.15.Bt, 12.20.Ds, 12.38.Bx