Topological exchange statistics in one dimension

The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this approach gives only trivial or near-trivial exchange statistics in one dimension because two-body coincidences are excluded from configuration space. Instead, we include these path-ambiguous singular points and consider configuration space as an orbifold. This orbifold topological approach allows unified analysis of exchange statistics in any dimension and predicts possibilities for anyons in one-dimensional systems, including non-Abelian anyons obeying alternate strand groups. These results clarify the nontopological origin of fractional statistics in one-dimensional anyon models.

Automated summary

The standard topological approach is limited in analyzing exchange statistics of indistinguishable particles in one dimension. By including path-ambiguous singular points and considering configuration space as an orbifold, a unified analysis of exchange statistics in any dimension becomes possible, predicting the existence of non-Abelian anyons in one-dimensional systems.