How can I develop a thesis about paranoia and hysteria in The Crucible?
Paranoia and hysteria are two states of mind that are powerfully expressed in this play. In order to develop a thesis that includes these two ideas, you will want to consider the context within which you want to discuss them. Do you wish to explore the presence of paranoia and hysteria in the play as it relates to the play's allegorical and parallel meaning, i.e., its representation of the McCarthy hearings and the surrounding fear and suspicion about Communism in America? If so, you'd want to portray these parallels somehow.
Or perhaps you want to explore paranoia and hysteria as they affect the events in the play directly, in the context of the Salem Witch Trials. Paranoia is expressed in a number of different situations by a number of characters, and that paranoia seems to take two forms. One, there is paranoia about witchcraft, and about who may be practicing it or wielding it to harm their neighbors. Two, there is paranoia about the motives and behavior of others. For example: Elizabeth Proctor is paranoid that Abigail is trying to have her accused of witchcraft so that she (Abby) can try to seduce John Proctor again. But in this case Elizabeth's paranoia turns out to be real.
The presence of hysteria is best exemplified in the courtroom scenes, where the girls take advantage of having an audience to playact in front of, behaving as if they are possessed and bewitched. The nature of hysteria is that it causes otherwise reasonable people to behave unreasonably because they are swept up in emotionally intense situations. Fear is one emotion that causes extreme reactions, and in this way paranoia (fear) and hysteria are closely linked together as motivating forces in the play.
I hope some of these ideas and connections help you with formulating your thesis. Good luck!