where R ˇ ˇ is R followed by a swap of the two objects. In one-dimensional quantum systems, R is the scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable. The Yang–Baxter equation also shows up when discussing knot theory and the braid groups where R corresponds to swapping two strands. Since one can swap three strands in two different ways, the Yang–Baxter equation enforces that both paths are the same.