  For the interacting Feynman propagator $ \Delta_{F,int}(x,y) $ of scalar
electrodynamics, we show that the sign property, $ \operatorname{Re}
i\Delta_{F,int} \geq 0 $, hinges on the reversibility of time evolution. In
contrast, $ \operatorname{Im} i\Delta_{F,int} $ is indeterminate. When we
switch to reduced dynamics under the weak coupling approximation, the positive
semidefinite sign of $ \operatorname{Re} i\Delta_{F,int} $ is generally lost,
unless we impose severe restrictions on the Kraus operators that govern time
evolution. With another approximation, the rotating wave approximation, we may
recover the sign by restricting the test functions to exponentials under
certain conditions.
