The Jaynes-Gibbs principle of maximal entropy and the non-equilibrium propagators of the O(N) phi^4 theory at large N

TL;DR

This paper introduces a new method using the Jaynes-Gibbs maximal entropy principle to compute non-equilibrium Green's functions in the large N limit of the O(N) phi^4 theory, integrating initial conditions into Dyson-Schwinger equations.

Contribution

It develops a novel approach to calculate non-equilibrium propagators by constructing the density matrix via maximal entropy and applying it directly to Dyson-Schwinger equations at large N.

Findings

Explicit evaluation of two-point Green's functions for specific initial states.

Demonstration of the method's applicability to non-equilibrium quantum field theory.

Potential for extending to other non-equilibrium systems.

Abstract

We present a novel procedure for calculating non-equilibrium two-point Green's functions in the $O(N) \phi^{4}$ theory at large $N$. The non-equilibrium density matrix $\rho$ is constructed via the Jaynes-Gibbs principle of maximal entropy and it is directly implemented into the Dyson-Schwinger equations through initial value conditions. In the large $N$ limit we perform an explicit evaluation of two-point Green's functions for two illustrative choices of $\rho$.