Non-Equilibrium Thermo Field Dynamics

TLDR

NETFD retains most properties of conventional quantum field theory, such as operator formalism, time‑ordered Green’s functions, and real‑time Feynman diagram techniques. The authors aim to establish NETFD as a fundamental framework for quantum field theory of open systems. NETFD is constructed from a thermal state in thermal‑Liouville space, introducing a quasi‑particle superoperator, and from coarse‑graining that projects out part of the space to incorporate dissipation. NETFD preserves the usual quantum field theory properties and allows definition of entropy for nonequilibrium states.

Abstract

A fundamental framework for the construction of a quantum field theory for open systems, which will be called non-equilibrium thermo field dynamics (NETFD), is built upon two concepts. One is the thermal state in the thermal-Liouville space, by which the quasi-particle superoperator is introduced generally from the thermal state condition. The other is the coarse graining which is realized by projecting out some partial space from the complete thermal-Liouville space, and by which the dissipation is introduced. Most properties of the usual quantum field theory (e.g., the operator formalism, the time-ordered formulation of the Green's functions, the Feynman diagram method in real time, etc.) are preserved in NETFD. The entropy for the nonequilibrium state can be also introduced in NETFD.