“…This is a generalization of the usual types of particles: bosons have α = 0 (symmetric wave functions) and their mean-field description is via models of the form (1.4), fermions have α = 1 (anti-symmetric wave functions) and appropriate models for them are Hartree-Fock functionals (see [Bac92,LS77,Lio87,Lio88,FLS15] and references therein). For general α one speaks of anyons [Kha05,Myr99,Ouv07,Wil90], which are believed to emerge as quasi-particle excitations of certain condensedmatter systems [ASW84,Hal83,Hal84,ZSGJ14,CS15,LR16].…”