Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-03-20
Phys.Lett. B357 (1995) 131-137
Physics
High Energy Physics
High Energy Physics - Theory
13p. latex (Revtex), no figures.
Scientific paper
10.1016/0370-2693(95)00863-G
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 $\gamma \rightarrow 0, (\infty$) 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.
Gamboa Jorge
Zanelli Jorge
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