Just recently I happened to come across a related problem. I would be interested in some comments on the below, related phenomenon

[juicemission]

Describe the bug
In QFT, in a Lorentz signature setting, one can define two kind of quantum field correlator function(al)s: simple VEV of products of the quantum field operator (let us call them Wightman correlators), and the VEV of time ordered products of the quantum field operator (let us call them Feynman correlators). The Wightman correlators are the ones which satisfy the Wightman axioms, including the Wightman positivity. (If Wick rotated, they will satisfy the Osterwalder-Schraeder axioms, including the OS positivity, or reflection positivity.) The Feynman correlators, however, are the ones which are in principle returned by a Feynman integral procedure. Also, these are the ones, which turn up when one would like to evaluate QFT predictions (S matrix, for instance). To me, it seems that the transition from Wightman correlators to Feynman correlators is basically a projection (time ordering). So, if I am not mistaken, Wightman correlators (without bringing in some external information) cannot be fully recovered from merely the Feynman correlators. The question naturally arises: to what extent the Wightman axioms (in particular, the Wightman positivity) are reflected in the properties of the Feynman correlators? (We should not assume, of course, anything to be known about the theory, except for its Feynman correlators.)

To Reproduce
1. Set up a scenario in the QFT module to compute and compare both Wightman and Feynman correlators.
2. Execute the calculation of the Wightman correlators ensuring they comply with the Wightman axioms.
3. Run the Feynman integral procedure to obtain the Feynman correlators.
4. Analyze the resulting Feynman correlators to determine if the Wightman axioms, particularly positivity, are reflected.
5. Document any observed deviations that suggest a loss of Wightman properties.

Expected Behavior
The expectation is that the Wightman axioms should inherently apply to the properties of the Feynman correlators, especially when no external information is provided. The software should thus reflect this theoretical expectation, maintaining the integrity of QFT principles when making any predictions or when evaluated for physical scenarios.

Screenshots
Not applicable due to the theoretical nature of the bug report.

Environment

Arch Linux

[Marioood]

Incorrect wording, Bug report should have "QFT" substituted with "$DOGE" and "Feynman" with "Wojaks".