Abstract We revisit the TFD formulation for finite-temperature field theory and demonstrate its fundamental role in grasping key aspects of real-time finite-temperature field theory. Specifically, we demonstrate that the general unitary SU (1,1) formulation of TFD, in which the conjugation rules are redefined, is consistent with the GNS construction and Tomita-Takesaki theory. We calculate the SU (1,1) thermal propagator and show that the KMS condition is independent of the choice of the SU (1,1) parameters.
Gadelha et al. (Sat,) studied this question.