Comment on the paper SciPost Phys. Core 6, 019 (2023) by Jo\~ao F. Melo (arXiv:2112.09119)

In the paper by Jo\~ao F. Melo "The propagator matrix reloaded" (SciPost Phys. Core 6, 019 (2023), arXiv:2112.09119) the author provides a derivation of a formalism which includes interactions in the initial conditions for non-equilibrium quantum field theory. The main statement of this paper is that one cannot ignore interactions in the initial conditions, so quantum field theories at finite temperature are not free in the infinite past. In this comment we revise in details calculations from the section 5 of the paper and demonstrate explicitly that the main statement of this paper should be reconsidered.