Did your wife and you have any sort of an agreement for how you'd handle dating others during your separation? If you didn't, then there's really not much you can do or say -- there's nothing to "forgive."
btw, why do you "believe" her when she says their affair wasn't physical? Even if it was, you guys can get thru this; there are ways to deal with the hurt and the resentment and the damage, if both parties are committed to it.
