ec 2 00 3 Hydrostatic pressure of the O ( N ) φ 4 theory in the large N limit

With non–equilibrium applications in mind we present in this paper (first in a series of three) a self–contained calculation of the hydrostatic pressure of the O(N) λφ4 theory at finite temperature. By combining the Keldysh–Schwinger closed–time path formalism with thermal Dyson–Schwinger equations we compute in the large N limit the hydrostatic pressure in a fully resumed form. We also calculate the high–temperature expansion for the pressure (in D = 4) using the Mellin transform technique. The result obtained extends the results found by Drummond et al. [1] and Amelino–Camelia and Pi [2]. The latter are reproduced in the limits mr(0)→0, T →∞ and T →∞, respectively. Important issues of renormalizibility of composite operators at finite temperature are addressed and the improved energy–momentum tensor is constructed. The utility of the hydrostatic pressure in the non–equilibrium quantum systems is discussed. PACS: 11.10.Wx; 11.10.Gh; 11.15.Pg