Two-particle scattering theory for anyons

We consider potential scattering theory of a nonrelativistic quantum mechan ical 2-particle system in R-2 with anyon statistics. Sufficient conditions are given which guarantee the existence of Moller operators and the unitari ty of the S-matrix. As examples the rotationally invariant potential well a nd the delta-function potential are discussed in detail. In case of a gener al rotationally invariant potential the angular momentum decomposition lead s to a theory of Jost functions. The anyon statistics parameter gives rise to an interpolation for angular momenta analogous to the Regge trajectories for complex angular momenta. Levinson's theorem is adapted to the present context. In particular we find that in case of a zero energy resonance the statistics parameter can be determined from the scattering phase. (C) 1999 American Institute of Physics. [S0022-2488(99)01504- 2].