I understand this question has already been asked here, however, I don't have enough reputation points to place a comment (I suppose that's the reason) on a specific answer to request a reference.
A user has answered (I'm not sure I can cite his name here, so I won't):
There is one technical inaccuracy in saying that antimatter moves back in time (whatever it might mean). In quantum field theory we get positive energy solutions (usual particles) and negative energy solutions. Negative energy solutions behave in time as if they were propagating backward in time. But they are not the antiparticles, they are just the "negative-energy particles". Antiparticles are positive energy solutions, and they are obtained by acting with charge conjugation operator on the negative-energy solutions. So, antiparticles move forward in time, as usual particles.
and, even though someone else comments
This is interpreting "going back in time" differently than anyone else does.
I'd like a reference for (or further clarification on) that, since I have already heard that before (also informally).
I understand this is a repost but if someone could at least give me some reference before closing it, I'd be thankful.
PS: My first intention was to ask how to proceed on this case in "meta", but I don't have reputation points to place a question there.
To clarify further my question: I had originally the same question as the OP from the post I quoted. At first, I thought that an explanation of what are anti-particles and the interpretation as particles going back in time could be found in quantum mechanics alone, without more advanced quantum field theory. The argument I knew is that anti-particles are really related to the originally negative-energy solutions, that can be reinterpreted as positive-energy solutions, as long as one invert the sign of time in the unitary time-evolution operator. This would hence lead to the reinterpretation of such states as positive-energy anti-particles going back in time or, at least, with anomalous time dependency.
The particular answer I quoted, seems to contradict this interpretation, saying that it is a mistake. I'd like a further clarification here. Is this interpretation really wrong?
From what is said on Wikipedia, looks like the Feynman–Stueckelberg interpretation relies on the fact that anti-particles are to be understood as particles going backwards in time and then related to the latter by charge conjugation.
Where does this interpretation primordially comes from? Where is it primordially needed if their association with the negative energy solutions of Dirac's equation (say) is a mistake? I understand that in quantum field theory one uses complex fields to describe both particles and anti-particles, relating them by charge conjugation. But isn't this done this way to accommodate Feynman–Stueckelberg's interpretation?