Insights What is the explanation for the existence of anyons in 2 dimensions?

[A. Neumaier]

we have 2 different particles, that individually are either bosons or fermions?

No. A single particle alone in the world is neither boson nor bermion nor anyon. The latter are properties of the corresponding many-body system.

 

[Demystifier]

Hi! I am new to this topic and a bit confused. In the normal boson and fermions statistics, as you said, we have identical particles. So, depending whether the wave function is symmetric or not, we can argue that that particle is a boson or fermion. But in the example you gave, if instead of $\pm 1$ we have another factor, we have an anyon. But you also said that this is the case only if the 2 particles are not identical, so we can have an asymmetric potential. So what exactly is called an anyon, as we have 2 different particles, that individually are either bosons or fermions? Is the wave function itself that is called anyon? Thank you!

The two particles, which in the absence of this specific interaction would behave as bosons or fermions, behave as two anyons due to interaction. Since they behave as two anyons, it is common to say that they "are" two anyons.