U(1) group

The U(1) group is a mathematical concept used in physics to describe symmetry in certain systems, especially in quantum mechanics and electromagnetism. It represents all rotations or transformations that leave a system unchanged when performed in a specific way—specifically, adding a phase factor (a kind of angular shift) that varies continuously from 0 to 2π. Think of it like rotating a circle: rotating by any angle won't change the circle's appearance. In physics, U(1) underpins the electromagnetic force, describing how electric and magnetic fields behave under these continuous, symmetrical transformations.