What are the conditions for the slaughterer according to the Four Schools of Thought?

For the slaughter to be valid, there are conditions related to the slaughterer: they must be sane, Muslim or from the People of the Book, not in a state of ihram if slaughtering land game, and they must pronounce the name of Allah over the animal at the time of slaughter, when remembering and able. They must also not slaughter in the name of anyone other than Allah.