Anyons in 1 + 1 Dimensions

The possibility of excitations with fractional spin and statististics in 1+1 dimensions is explored. The configuration space of a two-particle system is the half-line. This makes the Hamiltonian self-adjoint for a family of boundary conditions parametrized by one real number γ. The limit γ → 0, (∞) reproduces the propagator of non-relativistic 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 dimensions. These checks support validity of the interpretation of γ as a parameter related to the “spin” that interpolates continuously between bosons (γ = 0) and fermions (γ = ∞). Our approach can thus be useful for obtaining the propagator for one-dimensional anyons. Typeset using REVTEX E-mail: [email protected] E-mail: [email protected], [email protected] 1