Infrared catastrophe in a massless Feynman function
A new kind of infrared catastrophe is discussed. Like the traditional infrared divergence it is a problem at the level of the amplitude not the probability. It arises from inserting an internal photon line into a Feynman diagram having no external charged-particle lines. The resulting Feynman function is well defined, but the small \(k\)-contributions convert the normal singularity along the Landau-Nakanishi singularity surface to a singularity of stronger kind [cf. \textit{L. D. Landau}, Nuclear Phys., 13, 183-192 (1959); \textit{N. Nakanishi}, Prog. Theor. Phys., 22, 128-144 (1959)]. This stronger singularity is incompatible with the known fall- off properties of charged particle propagators at large distances. This situation is examined in a concrete situation, with emphasis on the microlocal aspect. Although the microlocal simplicity of a holonomic system which characterizes a Feynman function is widely observed in the massive case, such simplicity can be destroyed by the insertion of a massless line.
Feynman diagram having no external charged-particle lines
microlocal simplicity of a holonomic system
scientific article; zbMATH DE number 683170