Pressure of the Non-equilibrium O(N) Phi^{4} Theory in the Large N Limit

TL;DR

This paper calculates the non-equilibrium hydrostatic pressure in the large N limit of the O(N) Phi^4 theory using Green's functions and the Kadanoff-Baym equations, providing explicit solutions for different initial conditions.

Contribution

It introduces a method to compute non-equilibrium pressure in the O(N) Phi^4 theory using the large N limit and Green's functions, extending previous equilibrium approaches.

Findings

Pressure expressed in terms of two-point Green's functions.

Exact solutions to Kadanoff-Baym equations for specific initial states.

Explicit pressure calculations for three different initial density matrices.

Abstract

We calculate the off-equilibrium hydrostatic pressure for the O(N) Phi^{4} theory to the leading order in 1/N. The present paper, the first of a series, concentrates on the calculation of pressure in the non-equilibrium but translationally invariant medium. The Jaynes-Gibbs principle of maximal entropy is used to introduce the relevant density matrix which is then directly implemented into dynamical equations through generalised Kubo-Martin-Schwinger (KMS) conditions. We show that in the large N limit use of Ward identities enables the pressure to be expressed in terms of two point Green's functions. These satisfy the Kadanoff-Baym equations which are exactly solvable, and we explicitly calculate the pressure for three illustrative choices of \rho.