Francesco Toppan
A colored look at anyons and parastatistics
Paraparticles beyond bosons/fermions belong to two main classes: the anyons, which are exchanged under the braid group and exist up to $2$ space dimensions, and the paraparticles, theoretically possible in any space dimension, exchanged via the permutation group. For both classes, parabosonic and parafermionic particles can be found, with parafermions satisfying a (generalized) Pauli exclusion principle. A natural way to accommodate these parastatistics is via Rittenberg-Wyler's framework of color Lie (super)algebras graded by abelian groups. The first theoretical signature of paraparticles living in any space dimension was produced for ${\bf Z}_2\times {\bf Z}_2$-graded parafermions. More general grading groups, such as ${\bf Z}_3\times {\bf Z}_3$, allow to accommodate anyons in the RW's framework.
A state of the art of theoretical and experimental advances is briefly recalled.
