Anyons in 1+1 Dimensions

Abstract

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 $\gamma$. The limit $\gamma \to 0,(\infty$) 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 $\gamma$ as a parameter related to the ``spin'' that interpolates continuously between bosons ($\gamma =0$) and fermions ($\gamma =\infty$). Our approach can thus be useful for obtaining the propagator for one-dimensional anyons.

13p. latex (Revtex), no figures.

References in corpus (4)

• Neutral and Charged Anyon Fluids
• Multivalued Fields on the Complex Plane and Conformal Field Theories
• Self-Intersection, Axial Anomaly and the String Picture of QCD
• Multivalued Fields on the Complex Plane and Braid Group Statistics

Cited by in corpus (6)

• Three aspects of bosonized supersymmetry and linear differential field equation with reflection
• Cubic root of Klein-Gordon equation
• Quantum oscillator as 1D anyon
• Path Integral on Star Graph
• Global Anomalies and Anyons in 1+1 Dimensions
• One-dimensional anyons in relativistic field theory