Can a woman's body react as if it is pregnant enough to even test positive on a pregnancy test without sperm?

I don't want to seem naive, but I have had a vasectomy and have been tested afterward and have a zero count. My girl tested positive once and negative once with tests and said she had a miscarriage of sorts and her body's chemistry mixed with my own are super compatible and her body reacted as if it was pregnant even though she couldn't have actually been pregnant. I can't seem to find anything about this to see if it's possible. Any clues?