A COMPARISON OF THE REAL-TIME AND THE IMAGINARY-TIME FORMALISMS OF FINITE-TEMPERATURE FIELD-THEORY FOR 2-POINT, 3-POINT AND 4-POINT GREEN-FUNCTIONS

We compare the predictions of the real-time and the imaginary-time formalisms of finite temperature field theory. We construct, in the real-time formalism, retarded and advanced amplitudes which are linear combinations of the usual time-ordered thermo-field dynamics amplitudes. These amplitudes can be easily compared to the various analytically continued amplitudes of the imaginary-time formalism. Explicit calculation of the 2, 3 and 4-point Green functions in phi-3 field theory is done in the one and two-loop approximations and the compatibility of the two formalisms is shown.