An equivalence class of quantum field theories at finite temperature

Abstract
It is shown that there exists a certain equivalence class of quantum field theories at finite temperature each of which produces the same statistical averages. The theories in this equivalent class are classified by multiplicities of field degrees of freedom and have a one to one correspondence with the choices of the path in the real-time path-ordered formulation of the statistical average. Among them, thermo field dynamics is found to be the most convenient theory.