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I have the same problem, with the belief in cheating girlfriends.  There is really no way to convince him, he has to come to terms with the reality that his disease is making him see things where no thing exists.  The sad fact is that he may not ever be able to.  In his mind you have done everything he has accused you of, and the emotional tragedy of his false belief is as real as if it had truly happened.  As to the social life, it will most likely come and go, so if you want to remain with him, there are two things you will have to accept--he will think you are cheating and will lash out because of the pain it causes, even if he was shown incontrovertable truth that it isn't so--and he will vehemently oppose all the normal social interactions you desire.  The two go hand in hand, because for him, to go out, is to suffer even more emotional damage from your phantom cheating.  Just remember it isn't your fault, but it is your choice.  Is he worth it?