Exact Calculation of Ring Diagrams and the Off-shell Effect on the Equation of State

Abstract

The partition function with ring diagrams at finite temperature is exactly caluclated by using contour integrals in the complex energy plane. It contains a pole part with temperature and momentum dependent mass and a phase shift part induced by off-shell effect in hot medium. The thermodynamic potentials for ${\varphi }^4$ and ${\varphi }^3$ interactions are calculated and compared with the quasi-particle (pole) approximation. It is found that the off-shell effect on the equation of state is remarkable.

Comments: 7 pages, 11 figures, refereces added, final version to appear in PRD