N-particle sector of quantum field theory as a quantum open system

TL;DR

This paper presents a method using the Zwanzig projection formalism to derive evolution equations for the n-particle sector in quantum field theory, demonstrated with a scalar field with cubic interaction.

Contribution

It introduces a systematic approach to obtain the reduced density matrix evolution in quantum field theory sectors using projection techniques, with explicit perturbative derivation.

Findings

Derived the master equation at lowest non-zero order in perturbation theory.

Applied the formalism to a scalar $g \, \phi^3$ interaction model.

Provided a framework for analyzing open quantum systems in field theory.

Abstract

We give an exposition of a technique, based on the Zwanzig projection formalism, to construct the evolution equation for the reduced density matrix corresponding to the n-particle sector of a field theory. We consider the case of a scalar field with a $g \phi^3$ interaction as an example and construct the master equation at the lowest non-zero order in perturbation theory.