Yo. I work in the field of quantum information. Usually you think of two different types of particles, fermions and bosons which loosely correspond to matter an

Yo. I work in the field of quantum information. Usually you think of two different types of particles, fermions and bosons which loosely correspond to matter and force mediating particles. Electrons are fermions, and photons for instance are bosons. Quarks are fermions and gluons are bosons of the strong force. If I take two bosons and pick them up and switch their locations, then nothing happens. If I have two fermions on the other hand and switch their locations, their wave functions will acquire a 180 degree phase shift (or sign flip, as you please) relative to the collective wavefunction of the two particles in their original place. Anyons are particles that acquire an arbitrary phase shift under exchange. You might call exchange braiding in 2D, since you really are forced to make the particles go AROUND each other. If you do the motion that people do when playing the 3 shell game, if you think of the position of the particles' location plotted in time, you'd kinda see a rope being braided out. A nonabelian anyion is one for which the exchange is non-commutative. If I braid A around B which has been braided around C, it's different than braiding B around A which has been braided around C. Non-abelian just in general means non-commutative, which just means that it's different if you do things in a different order.