Abstract
The best known theory with massless particles is quantum electrodynamics (QED). The masslessness of the photons leads to infrared (UR) singularities the Green’s functions have near the electron mass shell. These singularities1 are gotten correctly only by summing over all orders of perturbation theory as far as the soft-photon effects are concerned. I will describe UR singularities in theories with scalar neutral self-coupled massless particles. Also here the singularities are gotten correctly only by summing over all orders of perturbation theory, and again it suffices to do so with respect to the soft-massless-particle effects. Apart from this, the singularities have no relation nor resemblence to those in QED. They play a role in the quantum field theoretical treatment of some problems2 in statistical mechanics, but not in particle physics since we know no such massless particles. The reason for studying such singularities goes back to large-momenta-behaviour problems as I will briefly explain at the end.
Published Version
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