of various Minkowskian correlators (retarded, advanced, time-ordered, etc.) at nonzero temperature can only be reproduced using the Feynman rules of the full real-time formalism, featuring, in particular, a doubling of field variables. Trying to gain a detailed understanding of the conditions, under which the full real-time formalism reduces to its naive version, is clearly an intriguing avenue for future research.

Acknowledgments {#acknowledgments .unnumbered}
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IG and AV were supported in part by the Academy of Finland, grant no. 1273545 and 1303622. PR was supported in part by the Department of Energy, DOE, award no. DE-SC0008132.

On the choice of loop momenta \[sec:mom\]
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When expressing an $N$-loop Feynman diagram in momentum space, there are a number of possible choices for the integration (or loop) momenta. We choose each of them to correspond to the momentum flowing along one of the propagators, in which case their assignment is limited by two rules, both related to momentum conservation:

1.  All internal lines meeting at a given vertex or subdiagram cannot be chosen to correspond to independent loop momenta, as they are linearly dependent.

2.  For each closed loop in the graph, at least one of the propagators forming the loop must be 