We investigate the weak-coupling expansion at high temperature for relativistic quantum field theories. Boson self-energies generally acquire a non-analytic dependence on the coupling due to the infrared plasmon effect. We show how to sum loops within loops for such thermodynamic quantities as pressure and energy density. Recent high-precision Monte Carlo simulations of quarkless SU(3) gauge theory are compared to the weak-coupling expansion and an excellent agreement is obtained for the high-temperature phase. Weak-coupling calculations are also carried out for supersymmetric grand unified models. We find indications that such models are often strongly coupled already at the unification temperature. This may have a significant effect on models of the early universe.
Bibliographical noteFunding Information:
We thank H. Goldbergf or helpful and instructivec onversationDs.. B.R. and S.R. wish to thank the Lewes Centerf or Physics,w herepart of this work was done, for its hospitalitya nd excitinga tmosphereT.h e work of J.K. was supportedin part by the Departmenot f Energy contract DOE/DE-AC02-79ER-10364T.h e work of D.B.R. and S.R. was supportedin part by the Departmenot f Energy contract DE-AC02-83ER40105T.h e work of S.R. was also supporteidn part by a Presidential Young InvestigatoArw ard.