Using the braid-group formalism we study the consequences of gauge invariance for fractionally charged anyonic quasiparticles in a two-dimensional multiply connected system. It is shown that gauge invariance requires multicomponent wave functions, and leads to the emergence of a hidden topological ${\mathit{Z}}_{\mathit{n}}$ symmetry with associated quantum number and unavoidable occurrence of level crossings for many-body eigenstates. In certain situations, it relates the fractional charge to anyon statistics. The implications for the fractional quantum Hall effect are also discussed.

• Received 13 August 1990

DOI:https://doi.org/10.1103/PhysRevLett.66.659