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Scattering states of plektons (particles with braid group statistics) in 2+1 dimensional quantum field theory

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Abstract

A Haag-Ruelle scattering theory for particles with braid group statistics is developed, and the arising structure of the Hilbert space of multiparticle states is analyzed.

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References

  1. Artin, E.: In: Lang, S., Tate, J.E. (eds.) The collected papers of E. Artin. Reading, MA: Addison-Wesley, 1965

    Google Scholar 

  2. Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1–54 (1982).

    Google Scholar 

  3. Doplicher, S., Haag, R., Roberts, J.E.: Local Observables and particle statistics I+II. Commun. Math. Phys.23, 199–230 (1971) and 35, 49–85 (1974)

    Google Scholar 

  4. Doplicher, S., Roberts, J.E.: Why there is a Field Algebra with a Compact Gauge Group Describing the Superselection Structure in Particle Physics. Commun. Math. Phys.131, 51–107 (1990)

    Google Scholar 

  5. Fredenhagen, K.: On the existence of antiparticles. Commun. Math. Phys.79, 141–151 (1981)

    Google Scholar 

  6. Fredenhagen, K.: A Remark on the cluster theorem. Commun. Math. Phys.97, 461–463 (1985)

    Google Scholar 

  7. Fredenhagen, K.: Sum rules for spins in (2+1)-dimensional quantum field theory. In: Doebner, H.D., Hennig, J. (eds.) Quantum Groups. Proceedings, Quantum Group Workshop Clausthal 1989. Lecture Notes in Physics 370, Berlin, Heidelberg, New York: Springer 1990, pp. 340–348

    Google Scholar 

  8. Fredenhagen, K.: Generalizations of the theory of superselection sectors. In: Kastler, D. (ed.) The Algebraic Theory of Superselection Sectors, Singapore: World Scientific, 1990, pp. 379–387

    Google Scholar 

  9. Fredenhagen, K.: Global observables in local quantum physics. In: Araki, H., et al. (eds.) Quantum and Non-Commutative Analysis, Amsterdam: Kluwer, 1993, pp. 41–51

    Google Scholar 

  10. Fredenhagen, K., Rehren, K.-H., Schroer, B.: Superselection sectors with braid group statistics and exchange algebras. I: General theory, II: Geometric aspects and conformal covariance. Commun. Math. Phys.125, 201–226 (1989) and Rev. Math. Phys., Special Issue (1992) 113–157

    Google Scholar 

  11. Fröhlich, J., Marchetti, P.A.: Spin-statistics theorem and scattering in planar quantum field theories with braid statistics. Nucl. Phys.B356, 533–573 (1991)

    Google Scholar 

  12. Gaberdiel, M.: Zopfgruppenstatistik in der Quantenmechanik und in der algebraischen Quantenfeldtheorie. Diploma thesis, Universität Hamburg, 1992

  13. Guido, D., Longo, R.: Relativistic invariance and charge conjugation in quantum field theory. Commun. Math. Phys.148, 521–551 (1992)

    Google Scholar 

  14. Haag, R.: Quantum field theories with composite particles and asymptotic completeness. Phys. Rev.112, 669–673 (1958); Ruelle, D.: On the asymptotic condition in quantum field theory. Helv. Phys. Acta 35, 147–163 (1962)

    Google Scholar 

  15. Haag, R.: Local Quantum Physics. Berlin, Heidelberg, New York: Springer, 1992

    Google Scholar 

  16. Laughlin, R.B.: Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations. Phys. Rev. Lett.50, 1395–1398 (1983); Fröhlich, J., et al.: The fractional quantum Hall effect, Chern-Simons theory, and integral lattices. Preprint, ETH-TH/94-18

    Google Scholar 

  17. Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento 37B, 1–23 (1977)

    Google Scholar 

  18. Longo, R.: Index of subfactors and statistics of quantum fields I+II. Commun. Math. Phys.126, 217–247 (1989) and 130, 285–309 (1990)

    Google Scholar 

  19. Mack, G., Schomerus, V.: Conformal field algebras with quantum symmetry from the theory of superselection sectors. Commun. Math. Phys.134, 139–196 (1990)

    Google Scholar 

  20. Mund, J., Schrader, R.: Hilbert spaces for nonrelativistic and relativistic “Free” Plektons (particles with braid group statistics). SFB 288 Preprint No. 74 (1993)

  21. Reed, M., Simon, B.: Methods of modern mathematical physics. III Scattering Theory. New York: Academic Press, 1979

    Google Scholar 

  22. Rehren, K.-H., Schroer, B.: Einstein causality and Artin braids. Nucl. Phys.B312, 715–750 (1989)

    Google Scholar 

  23. Rehren, K.-H.: Field operators for anyons and plektons. Commun. Math. Phys.145, 123–148 (1992)

    Google Scholar 

  24. Roberts, J.E.: In preparation

  25. Rüger, S.M.: Streutheorie für Teilchen mit Zopfgruppenstatistik. Diploma thesis, FU Berlin, 1990

  26. Schroer, B.: Scattering properties of anyons and plektons. Presented at the “XXIV Symposion of the theory of elementary particles”, in Gosen, Berlin, 1990

  27. Steenrod, N.: The Topology of Fiber Bundles. Princeton, NJ: Princeton University Press, 1951

    Google Scholar 

  28. Schrader, R.: Notes on Hilbert spaces with braid group statistics. Unpublished notes 1989

  29. Tscheuschner, R.D.: Topological Spin-Statistics relation in quantum field theory. Int. J. Theor. Phys.28, 10, 1269–1310 (1989)

    Google Scholar 

  30. Wilczek, F.: Quantum Mechanics of Fractional-Spin Particles. Phys. Rev. Lett.49, 957–959 (1982)

    Google Scholar 

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Communicated by G. Felder

Partly supported by ‘Studienstiftung des deutschen Volkes’.

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Fredenhagen, K., Gaberdiel, M.R. & Rüger, S.M. Scattering states of plektons (particles with braid group statistics) in 2+1 dimensional quantum field theory. Commun.Math. Phys. 175, 319–335 (1996). https://doi.org/10.1007/BF02102411

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  • DOI: https://doi.org/10.1007/BF02102411

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