"Under what set of laws is "invading one's private space" illegal?"
Under Texas law, Chapter 4892, one's private space is the length of one's arm plus 12" and when someone violates your space, you have the right, and indeed the duty, to teach him manners by decking him. Of course, if that someone is female, then your duty is to kiss them (but then she can deck you for violating her space, LOL). /humor