INFRARED PROBLEM IN G-PHI-4 THEORY AT FINITE TEMPERATURE

We study the infrared problem in gφ4 theory in 4 dimensions at finite temperature in the context of the real-time formalism. We perform a complete 2-loop analysis of the mass shift in this model, as an N-loop calculation for a specific class of diagrams. In the case of massless particles, we find the same problems as for hot QCD, that is, the natural infrared cutoff which emerges as a thermal mass, m2 ∼ gT2, is too small to act as a good cutoff and the perturbance theory breaks down beyond some order in the coupling constant g. However, we find that an explicit summation of the leading infrared divergent diagrams gives a result which is not very different from the perturbation approach. © 1990.