Hydrostatic Pressure of the O(N) $\phi^4$ Theory in the Large N Limit

TL;DR

This paper calculates the hydrostatic pressure of the O(N) $\,\phi^4$ theory at finite temperature using advanced field-theoretic methods, providing new insights into non-equilibrium quantum systems and extending previous results.

Contribution

It introduces a self-contained method combining the Keldysh-Schwinger formalism with Dyson-Schwinger equations to compute pressure in the large N limit, including high-temperature expansion.

Findings

Derived a fully resumed expression for pressure at large N

Extended previous high-temperature results with Mellin transform techniques

Addressed renormalizability of composite operators at finite temperature

Abstract

With non-equilibrium applications in mind we present in this paper a self-contained calculation of the hydrostatic pressure of the O(N)\lambda \phi^4 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. [hep-ph/9708426] and Amelino-Camelia and Pi [hep-ph/9211211]. The latter are reproduced in the limits m_r(0)\to 0, T \to \infty and T \to \infty, 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.