Chern-simons Field Theory and Generalizations of Anyons

It is well known that charges coupled to a pure Chern-Simons gauge field in (2+1) dimensions undergo an effective change of statistics, i.e., become anyons. We will consider several generalizations thereof, arising when the gauge field is more general. The first one is “multispecies anyons”—charged particles of several species coupled to one, or possibly several, Chern-Simons fields. The second one is finite-size anyons, which are charged particles coupled to a gauge field described by the ChernSimons term plus some other term. In fact, rigorously speaking, quasielectrons and quasiholes in the fractional quantum Hall effect are multispecies finite-size anyons. The third one is an analog of finite-size anyons which arises in a model with a mixed Chern-Simons term; notably, this model is P,T-invariant, which opens the way for practical applications even when there is no parity-breaking magnetic field.