Density matrix formalism for interacting quantum fields

TL;DR

This paper introduces a density matrix formalism for interacting quantum fields, enabling analysis of non-equilibrium processes and particle interactions in a momentum basis, with applications to open quantum systems.

Contribution

It develops a practical formalism for computing density matrix elements of interacting scalar fields using non-equilibrium quantum field theory techniques.

Findings

Formalism for density matrices in interacting quantum fields

Application to scalar field interactions and non-equilibrium processes

Framework for studying particle creation and annihilation at finite times

Abstract

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar-scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo field dynamics and the Schwinger-Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at finite times and other non-equilibrium processes including those found in the theory of open quantum systems.