Communications in Mathematical Physics

, Volume 286, Issue 3, pp 1159–1180 | Cite as

The Spin-Statistics Theorem for Anyons and Plektons in d = 2+1

Article

Abstract

We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass spectrum of the corresponding charged sector, and a restriction on the degeneracy of the corresponding mass.

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References

  1. 1.
    Binegar B.: Relativistic field theories in three dimensions. J. Math. Phys. 23, 1511 (1982)CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Buchholz D., Epstein H.: Spin and statistics of quantum topological charges. Fysica 17, 329–343 (1985)Google Scholar
  3. 3.
    Buchholz D., Fredenhagen K.: Locality and the structure of particle states. Commun. Math. Phys 84, 1–54 (1982)MATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Doplicher S., Haag R., Roberts J.E.: Local observables and particle statistics I. Commun. Math. Phys. 23, 199 (1971)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Doplicher S., Haag R., Roberts J.E.: Local observables and particle statistics II. Commun. Math. Phys. 35, 49–85 (1974)CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Fredenhagen K.: On the existence of antiparticles. Commun. Math. Phys 79, 141–151 (1981)CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Fredenhagen, K.: Sum rules for spins in (2+1)-dimensional quantum field theory. In: Quantum Groups, Berlin-Heidelberg-New York: H.D. Doebner et al., ed., Lecture Notes in Physics, Vol. 370, Springer, 1990, pp. 340–348Google Scholar
  8. 8.
    Fredenhagen K., Gaberdiel M., Rüger S.M.: Scattering states of plektons (particles with braid group statistics) in 2+1 dimensional field theory. Commun. Math. Phys. 175, 319–355 (1996)MATHCrossRefADSGoogle Scholar
  9. 9.
    Fredenhagen K., Rehren K.-H., Schroer B.: Superselection sectors with braid group statistics and exchange algebras II: Geometric aspects and conformal covariance. Rev. Math. Phys. SI1, 113–157 (1992)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Fröhlich J., Gabbiani F.: Braid statistics in local quantum field theory. Rev. Math. Phys. 2, 251–353 (1990)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Fröhlich J., Marchetti P.A.: Spin-statistics theorem and scattering in planar quantum field theories with braid statistics. Nucl. Phys. B 356, 533–573 (1991)CrossRefADSGoogle Scholar
  12. 12.
    Haag, R.: Local quantum physics, Second ed., Texts and Monographs in Physics, Berlin-Heidelberg: Springer, 1996Google Scholar
  13. 13.
    Jackiw R., Nair V.P.: Relativistic wave equations for anyons. Phys. Rev. D 43, 1933 (1991)CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Longo, R.: On the spin-statistics relation for topological charges. In: Operator Algebras and Quantum Field Theory, S. Doplicher, R. Longo, J. Roberts, L. Zsido, eds., Cambridge, MA: Int. Press, 1997, pp. 661–669Google Scholar
  15. 15.
    Mund, J.: The CPT and Bisognano-Wichmann theorems for massive theories with braid group statistics in d = 2 + 1. In preparationGoogle Scholar
  16. 16.
    Mund, J.: Quantum Field Theory of Particles with Braid Group Statistics in 2+1 Dimensions. Ph.D. thesis, Freie Universität Berlin, 1998Google Scholar
  17. 17.
    Mund J.: Modular localization of massive particles with “any” spin in d = 2 + 1. J. Math. Phys. 44, 2037–2057 (2003)MATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    Mund, J., Rehren, K.-H.: Symmetries in QFT of lower spacetime dimensions. In: Encyclopedia of Mathematical Physics, J.-P. Françoise, G. Naber, T.S. Tsun, eds., Vol. 5, Amslevdom: Elsevier, 2006, pp. 172–179Google Scholar
  19. 19.
    Roberts J.E.: Local cohomology and superselection structure. Commun. Math. Phys. 51, 107–119 (1976)MATHCrossRefADSGoogle Scholar
  20. 20.
    Roberts, J.E.: Net cohomology and its applications to field theory. In: Quantum Fields – Algebras, Processes L. Streit, ed., Wien, New York: Springer, 1980, pp. 239–268Google Scholar
  21. 21.
    Roberts, J.E.: Lectures on algebraic quantum field theory. The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, D. Kastler, ed., Singapore - New Jersey-London-Hong Kong: World Scientific, 1990, pp. 1–112Google Scholar
  22. 22.
    Streater R.F., Wightman A.S.: PCT, spin and statistics, and all that. W. A. Benjamin Inc, New York (1964)MATHGoogle Scholar
  23. 23.
    Varadarajan V.S.: Geometry of quantum theory. Vol. II. Van Nostrand Reinhold Co, New York (1970)MATHGoogle Scholar

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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal de Juiz de ForaJuiz de ForaBrazil

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