Gerd Ludemann's vision/hallucination theory, which has since been republished in different formats, is not based on historical conclusions and evidence but rather on the author's own biases against the supernatural. This is clear in his statement that "David Hume already demonstrated that a miracle is defined in such a way that `no testimony is sufficient to establish it'." He later says that "the literal statements about the resurrection of Jesus . . . have lost their literal meaning with the revolution in the scientific picture of the world." Ludemann is starting from a presumption of naturalism and trying to squeeze the historical evidence into that model rather than following the evidence wherever it leads.
Hume's argument has been refuted multiple times, perhaps most recently and effectively by John Earman in Hume's Abject Failure: The Argument Against Miracles. Ludemann's commitment to Hume leads him to postulate outlandish theories based on discredited Freudian and Jungian psychoanalysis. According to Ludemann's speculation, Peter had a vision of Jesus which was brought on by his guilt over having betrayed him. When he spoke of this vision to others, they became "infected" somehow, leading to their own visions. He never does explain the naturalistic mechanism by which one person's vision can "infect" someone else. Certainly I have heard other people talk about visions, but it never induced one in me. Ludemann wants us to believe that Peter's vision infected dozens of other people to the point where they would sacrifice their freedom, property, and even their lives to tell others that Jesus had risen from the dead. To say that this thesis lacks sufficient explanatory power is a gross understatement.
But none of this explains the conversion of Saul of Tarsus, so Ludemann has another psychoanalytical theory for that. Saul suffered from some kind of "Christ complex" which is what led him to persecute the church, but then the inner conflict of his suppressed guilt resulted in a powerful vision which transformed him into the remarkable and tireless apostle to the Gentiles. Again Ludemann relies on Freudian pyschobabble in explaining all of this. Besides the obvious weakness of this theory, he also fails to show that Paul only had a vision. Ludemann engages in questionable exegesis of Paul's letters to show that Paul only claimed a vision. He goes so far as to suggest that Paul really was blinded on the Damascus road, and that this blindness was "hysterical blindness." This in itself shows another problem with Ludemann's approach: he approaches the evidence in an ad hoc manner as it suits him. Thus he considers Paul's blindness in Acts to be historical, but not the fact that Paul's companions were also affected by the phenomenon. No historical or evidential basis is given for this. He simply picks and chooses his evidence because it fits his theory that way. In the same way, Ludemann regards Peter's denial of Christ as historical but the discovery of the empty tomb by the women as not.
However, Ludemann is to be given credit in some respects. For example, he recognizes that the list of appearances given by Paul in 1 Cor. 15 is very early, dating back to within 2-3 years of the crucifixion. He recognizes that Paul's claim included seeing Jesus, and that other "vision" theories which only include a light but not the person of Christ are inadequate. However, his attempt to show that Paul's vision of Jesus was merely an internal, subjective experience rather than an objective one comes up short on exegetical and historical grounds.
Despite the one or two good points in the book, it is mostly a fairly desperate, ad hoc theory based on outdated and discredited psychoanalytical theories, and that treats the evidence inconsistently. Ludemann simply determines the final destination in advance and then tries to find some way to get there. It's actually a credit to the strength of the evidence for the Resurrection that he is compelled to create such an outlandish hypothesis. Ludemann's thesis is unpersuasive and is unlikely to convince even most skeptics. But for naturalistic explanations of the evidence for the Resurrection, it may be the best that skeptics can come up with.