U(1) symmetry

U(1) symmetry refers to a type of mathematical invariance in physics where certain properties of a system remain unchanged when a specific phase (or angle) is rotated uniformly. Imagine a circle representing all possible phases; shifting all points by the same angle doesn’t alter the system's fundamental behavior. In particle physics, this symmetry underpins electromagnetism, where the electromagnetic interactions stay consistent under such phase rotations, leading to the existence of the photon as the force carrier. It’s a foundational concept that helps explain how certain forces and particles behave consistently under transformation.