AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ⁴ THEORY AT FINITE TEMPERATURE

The λϕ 4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < T c , this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.