Quantum electrodynamics at large distances. II. Nature of the dominant singularities.

Accurate calculations of macroscopic and mesoscopic properties in quantum electrodynamics require careful treatment of infrared divergences: standard treatments introduce spurious large-distances effects. A method for computing these properties was developed in a companion paper. That method depends upon a result obtained here about the nature of the singularities that produce the dominant large-distance behaviour. If all particles in a quantum field theory have non-zero mass then the LandauNakanishi diagrams give strong conditions on the singularities of the scattering functions. These conditions are severely weakened in quantum electrodynamics by effects of points where photon momenta vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared specifically to the pole-decomposition functions that dominate the macroscopic behaviour in quantum electrodynamics, and leads to strong results for these functions at points where photon momenta vanish. ∗This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098, and by the Japanese Ministry of Education, Science and Culture under a Grant-in-Aid for Scientific Research (International Scientific Research Program 03044078).