Simple logic tells us that Jesus could not have been walking around in a Roman province in a dead human body for forty days and nights without Romans seeing him; they'd have crucified him a second time and done whatever it took to ensure that he stayed crucified.
Nonetheless he did come back and to the people who witnessed it, what they witnessed was utterly indistinguishable from him having come back in his own body.
The mistake people make here is thinking that Jesus was the first and/or the only person ever to have been heard from after he died; he was the last. The OT contains a ghost story (1 Samuel 28:7 - 28:20 or thereabouts) in the familiar tale of Saul, Samuel, and the "witch of Endor" and in times more remote than that, such stories were less rare.
The resurrection was the sort of thing which Julian Jaynes described as "bicameral"; it was the last such thing ever seen by more than one or two people on our planet, and it was not any sort of an "auditory" or visual mass hallucination, but was sufficiently real.
I don't think this is factually correct. There was something different, he was not immediately recognizable to the witnesses.
How would they have done so?? Jesus' transfigured body could walk through walls and locked doors. Disappear from one local and immediately appear at another miles away. Methinks the Romans might have had just a "wee" bit of trouble hanging onto Him the second time around.