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Quantum mechanics and field theory with fractional spin and statistics

Stefano Forte*,†

Stefano Forte*,†

  • Service de Physique Théorique, C.E. Saclay, F-91191 Gif-sur-Yvette CEDEX, France

  • *On leave from I.N.F.N., Sezione di Torino, via P. Giuria 1, I-10125, Torino, Italy (present address).
  • †Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique.
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Rev. Mod. Phys. 64, 193 – Published 1 January, 1992

DOI: https://doi.org/10.1103/RevModPhys.64.193

Abstract

Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed.

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Rev. Mod. Phys. 64, 193– Published 1 January, 1992

    © 1992 American Physical Society

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