This is a follow up to this question: How to Perform Wick Rotation in the Lagrangian of a Gauge Theory (like QCD)?
I am wondering if their (6), using that $E^i_M = F^{0i}_M = i F^{0i}_E = i E^i_E$, implies that the electric field in Euclidean signature is changes sign under TR?
EDIT: My reasoning would be $E^i_M \overset{!}{=} T^{-1} E^i_M T = T^{-1} i E^i_E T = -i T^{-1} E_E^i T$, so that $T^{-1} E_E^i T = - E_E^i$ …
