ELI5: Explain Like I'm 5

Luttinger–Ward functional

So imagine you have a big toy box full of all your favorite toys. Now, let's say you want to organize all those toys in a way that makes it easy to find what you're looking for. That's kind of what the Luttinger-Ward functional does, but instead of toys, it's used to organize electrons.

Electrons are tiny particles that are found in atoms and they're kind of like the building blocks of matter. The Luttinger-Ward functional is a really fancy tool that helps scientists understand how these electrons behave and interact with each other.

It works like this: imagine you have a bunch of electrons in a big box. They're all bouncing around and interacting with each other in different ways. The Luttinger-Ward functional can help you figure out how these electrons will behave and what kind of properties they'll have.

To do this, the Luttinger-Ward functional uses a bunch of different math equations that take into account things like the energy and momentum of each electron. By putting all these equations together, you can get a really good idea of how those electrons are going to act and what kind of properties they'll have.

In the end, the Luttinger-Ward functional might not be something that you use every day in your life (unless you become a scientist who studies electrons!), but it's a really important tool for understanding how the world works on a super tiny scale.