How is the idea of guilt and sin developed in the scarlet letter?

Perhaps the foremost purpose of The Scarlet Letter is to illustrate the difference between shaming someone in public and allowing him or her to suffer the consequences of an unjust act privately. According to the legal statutes at the time and the prevailing sentiment of keeping in accordance with a strict interpretation of the Bible, adultery was a capital sin that required the execution of both adulterer and adulteress--or at the very least, severe public corporal punishment. Indeed, even if the husband wanted to keep his wife alive after she committed adultery, the law insisted that she would have to die for it. It is in this environment that Hester commits adultery with Dimmesdale, but we come to see that the public shaming cannot begin to account for all the complexities of the illicit relationship--or the context of it. What Hawthorne sets out to portray, then, is how the private thoughts, the private torture and guilt and emotional destruction of the people involved in the affair, are more than enough punishment for the crime. We wonder whether the state or society has any right to impose law in private matters between citizens. Does adultery really have no impact upon the lives of others? If not, it should not be seen as a crime against the village. A more charitable reading of the Bible would come later in reflections on the New Testament interpretation of adultery law, namely, that the public need not step in to punish a crime when we ourselves have our own sins to be judged. Each person suffers enough already for his or her own sins.