Geometrical meaning of braid statistics in (1+1)- and (2+1)-dimensional quantum field theory

Abstract

Braids naturally arise as topological objects in the discussion of statistics in quantum mechanics of indistinguishable pointlike particles moving in a (2+1)-dimensional space-time. Conversely, they also play a role as algebraic invariants in the discussion of superselection rules in (1+1)-dimensional algebraic quantum field theory. Here we show how Abelian braid statistics in (1+1) dimensions may be interpreted geometrically by introducing the concept of antiparticles, thus clarifying the connection between the two approaches.