ANYONS IN 1+1-DIMENSIONS

The possibility of excitations with fractional spin and statistics in 1 + 1 dimensions is explored. The configuration space of a two-particl e system is the half-line. This makes the Hamiltonian self-adjoint for a family of boundary conditions parametrized by one real number gamma . The limit gamma --> 0 (infinity) reproduces the propagator of non-re lativistic particles whose wavefunctions are even (odd) under particle exchange. A relativistic ansatz is also proposed which reproduces the correct Polyakov spin factor for the spinning particle in 1 + 1 dimen sions. These checks support the validity of the interpretation of gamm a as a parameter related to the ''spin'' that interpolates continuousl y between bosons (gamma = 0) and fermions (gamma = infinity). Our appr oach can thus be useful for obtaining the propagator for one-dimension al anyons.