Phase operator formalism in thermo field dynamics

Yusuke Nakamura, Y. Yamanaka

ARIMITSU Toshihico, Hiroomi Umezawa, Y. Yamanaka

I. Hardman, Hiroomi Umezawa, Y. Yamanaka

Toshihico Arimitsu

H. Matsumoto, Yoshimasa Nakano, Hiroomi Umezawa

The tilde substitution law (which will be called in this paper the thermal state condition) plays an important role in determining the temperature-dependent ground state in thermo field dynamics (a real-time operator formalism of quantum field theory at finite temperature). Rules which define the phase conventions for the tilde substitution for any arbitrary Heisenberg operator are derived. These rules also lead to a clear correspondence between the perturbation series obtained in thermo field dynamics and the path-ordered formalism of the statistical average.

Hiroomi Umezawa, H. Matsumoto, M. Tachiki