ELI5: Explain Like I'm 5

Wigner–Weyl transform

The Wigner-Weyl transform is like a special way of describing things in quantum physics so that we can understand them better.

Think of a toy car moving back and forth on a table. We can describe its motion with two things: position and velocity. Position is where the car is on the table, while velocity is how fast it's moving and in which direction.

In quantum physics, things like electrons and atoms also move around, but they move in ways that are a little bit different from a toy car. They also have something called momentum, which is similar to velocity but also takes into account the fact that these tiny things can behave like both particles and waves. Trying to describe the motion of an electron using just position and velocity is like trying to explain how a basketball bounces using only the concepts of up and down. It's not enough.

That's where the Wigner-Weyl transform comes in. It's like a special way of combining position and momentum to describe the motion of tiny things like electrons. It's almost like using a different type of language that is easier for us to understand. This transform allows us to visualize the motion of these tiny things in a way that wasn't possible before.

So, if you hear someone talking about the Wigner-Weyl transform, just remember that it's a special way of describing how tiny things move around in a language that's easier for us to understand!