Accidental symmetry

In physics, particularly in renormalization theory, an accidental symmetry is a symmetry which is present in a renormalizable theory only because the terms which break it have too high a dimension to appear in the Lagrangian. In physics, particularly in renormalization theory, an accidental symmetry is a symmetry which is present in a renormalizable theory only because the terms which break it have too high a dimension to appear in the Lagrangian. In the standard model, the lepton number and the baryon number are accidental symmetries, while in lattice models, rotational invariance is accidental. The connection between symmetry and degeneracy (that is, the fact that apparently unrelated quantities turn out to be equal) is familiar in every day experience. Consider a simple example, where we draw three points on a plane, and calculate the distance between each of the three points. If the points are placed randomly, then in general all of these distances will be different. However, if the points are arranged so that a rotation by 120 degrees leaves the picture invariant, then the distances between them will all be equal (as this situation obviously describes an equilateral triangle). The observed degeneracy boils down to the fact that the system has a D3 symmetry.