Why do a group of people need permission to start a union? Can a group of people unionize without permission of their employer? Does the employer need to sign a form or something?

I thought unions were just groups of people who bargained with collective power. Why don't all researchers at these universities just use their abilities as leverage? Most people in universities are hired because they're one of a few thousand people in the world who are up to speed on a specific topic. That makes them very difficult to replace, one would think.