Gap equation in scalar field theory at finite temperature

Abstract

We investigate the two-loop gap equation for the thermal mass of hot massless $g^2{\varphi }^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution of the gap equation beyond $g^2$ order in perturbation theory. We have solved the gap equation and obtain the real and the imaginary part of the thermal mass which are correct up to $g^4$ order in perturbation theory.

13 pages, Latex with axodraw, Minor corrections, Appendix added

References in corpus (3)

• Resummation in a Hot Scalar Field Theory
• Threshhold Singularities and the Magnetic Mass in Hot QCD
• Introduction to Thermal Field Theory