ON THE RELATIONSHIP BETWEEN THERMO-FIELD DYNAMICS AND QUANTUM-STATISTICAL MECHANICS

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.