The Euler–Heisenberg Lagrangian is a mathematical formula used to describe how light and matter interact. It was created by two very smart physicists named Euler and Heisenberg.
Basically, the Euler–Heisenberg Lagrangian takes the idea of particles and waves working together and explains in mathematical terms how they do it. It explains that when light (like from the Sun) meets matter (like air or a solid), the light energy changes its shape and pushes on the matter to make it move around. The Euler–Heisenberg Lagrangian gives us a way to calculate how much the light and matter interact, and how much they make each other move. It can also be used to help predict the behavior of particles and waves in different kinds of systems.