For a Minkowski spacetime of dimension three, particles of arbitrary, real spin and intermediate ( 0 -) statistics, called 'anyons', are studied within the framework of relativistic quantum field theory. The localization properties of interpolating fields for anyons and the relation between the spin of anyons and their statistics are discussed on general grounds. A model of a quantum field theory exhibiting anyons is described. Our results might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of high-Tc superconductors.
1. What are Anyons ?
In three spacetime dimensions, the spin of a relativistic particle can be an arbitrary real number, and the statistics of particles can be intermediate between Bose and Fermi statistics. Particles with real spin and intermediate statistics have been called 'anyons'
by Wilczek [ 1 ]. He suggested that electrically charged magnetic vortices, occurring in certain Higgs models, may be examples of such particles. He recognized that if a magnetic vortex carries a fractional electric charge, its spin is fractional and its statistics cannot be Bose or Fermi statistics. These findings follow from studying a variant of the Aharonov-Bohm effect. A more mathematical analysis of the statistics of anyons in terms of representations of the braid groups [2] was presented by Y. S. Wu [3].
Recent interest in the physical properties of anyons has been triggered by developments in solid state physics: In the Laughlin approach [4] to the fractional quantum Hall effect, excitations carrying fractional charge and fractional angular momentum, whose statistics is intermediate between Bose and Fermi statistics, play a key role. Such excitations are also expected to arise in recent models of high T c superconductivity [5]. Generally speaking, anyons can appear in two-dimensional physical systems with a (hidden or manifest) local gauge symmetry and broken parity invariance.
In this Letter, we present a general discussion of anyons within the framework of local quantum theory. We discuss the localization properties of fields which have nonvanishing matrix elements between the vacuum and a one-anyon state with fractional spin r 89 We show that such fields cannot be localized in bounded regions of threedimensional spacetime (see Section 2). We then discuss the three-dimensional, noncompact Abelian Higgs model with a Chern-Simons term in the action which breaks parity and show that it describes particles with the properties of anyons (Section 3).