Hotδexpansion

The $\delta$ expansion, a novel perturbative scheme for quantum field theories, is investigated in the case of finite temperatures. For the exactly solvable example of the large-$N$ limit of massless scalar four-dimensional ${\phi }^4$ theory, the first two orders of the $\delta$ expansion are compared with ordinary perturbation theory which at finite temperature is infrared singular beyond one-loop order. The $\delta$ expansion gives results which are nonperturbative with respect to the coupling constant and which compare favorably with the exact solution. Most importantly, the $\delta$ series naturally solves the general infrared problem of perturbative high-temperature field theories.