Gauge Symmetry

Many important properties of particle physics involve what are called “gauge symmetries.” These have a somewhat different flavor from the more familiar symmetries we see around us. With regard to translational symmetry, we might say that an experiment performed at two different points should have the same result. With regard to gauge symmetry, we might say that these two different points are essentially the same point. Mathematically, we would say that we are “modding out” by some equivalence relation. One example of modding out would be to show the equivalence between all horizontal lines on the cylinder. A cylinder can be thought of as the product of a line and a circle. If every point of a circle labels a line (namely the one that passes through it). Consider a gauge symmetry which is rotating the cylinder along its circumference. If we identify this as a “gauge symmetry” we would be identifying all the points of the circle with each other. In other words, all the horizontal lines of the cylinder would be viewed as equivalent.