Id. Lawrie, ON THE RELATIONSHIP BETWEEN THERMO-FIELD DYNAMICS AND QUANTUM-STATISTICAL MECHANICS, Journal of physics. A, mathematical and general, 27(5), 1994, pp. 1435-1452
The relationship between two approaches to the study of non-equilibriu
m field theories, namely quantum statistical mechanics and thermo fiel
d dynamics, is investigated. The formalism of superoperators acting in
the Liouville space of density matrices is used to provide a detailed
translation between the two approaches. It is found that thermo field
dynamics is exactly equivalent to a restricted version of quantum sta
tistical mechanics, in which the initial density matrix is constrained
to be Gaussian. The dissipative perturbation theory developed within
thermo field dynamics is translated into the language of statistical m
echanics, and is found to be equivalent to that devised by the author
using the statistical-mechanical closed-time-path method, except that
the latter theory is not restricted to Gaussian initial states.