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Progress of Theoretical Physics

Nonequilibrium Vacuum in Thermo Field Dynamics

H. Matsumoto

Published Jan 1, 1988• 7 citations
Publisher

Abstract

In the framework of thermo field dynamics, the so-called thermal state conditions of the vacuum are extended from the equilibrium case to general cases in the Heisenberg picture. The formalism is shown to describe nonequilibrium phenomena of a quantum field system. It is shown that the causal formulation of a perturbation theory is developed. As an example of application of the perturbation theory, an effective Hamiltonian describing a reservoir effect is obtained.

DOI
10.1143/ptp.79.373

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In the framework of thermo field dynamics, the so-called thermal state conditions of the vacuum are extended from the equilibrium case to general cases in the Heisenberg picture. The formalism is shown to describe nonequilibrium phenomena of a quantum field system. It is shown that the causal formulation of a perturbation theory is developed. As an example of application of the perturbation theory, an effective Hamiltonian describing a reservoir effect is obtained.
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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.