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.
Similar content being viewed by others
References
Artin, E.: In: Lang, S., Tate, J.E. (eds.) The collected papers of E. Artin. Reading, MA: Addison-Wesley, 1965
Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1–54 (1982).
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)
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)
Fredenhagen, K.: On the existence of antiparticles. Commun. Math. Phys.79, 141–151 (1981)
Fredenhagen, K.: A Remark on the cluster theorem. Commun. Math. Phys.97, 461–463 (1985)
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
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
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
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
Fröhlich, J., Marchetti, P.A.: Spin-statistics theorem and scattering in planar quantum field theories with braid statistics. Nucl. Phys.B356, 533–573 (1991)
Gaberdiel, M.: Zopfgruppenstatistik in der Quantenmechanik und in der algebraischen Quantenfeldtheorie. Diploma thesis, Universität Hamburg, 1992
Guido, D., Longo, R.: Relativistic invariance and charge conjugation in quantum field theory. Commun. Math. Phys.148, 521–551 (1992)
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)
Haag, R.: Local Quantum Physics. Berlin, Heidelberg, New York: Springer, 1992
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
Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento 37B, 1–23 (1977)
Longo, R.: Index of subfactors and statistics of quantum fields I+II. Commun. Math. Phys.126, 217–247 (1989) and 130, 285–309 (1990)
Mack, G., Schomerus, V.: Conformal field algebras with quantum symmetry from the theory of superselection sectors. Commun. Math. Phys.134, 139–196 (1990)
Mund, J., Schrader, R.: Hilbert spaces for nonrelativistic and relativistic “Free” Plektons (particles with braid group statistics). SFB 288 Preprint No. 74 (1993)
Reed, M., Simon, B.: Methods of modern mathematical physics. III Scattering Theory. New York: Academic Press, 1979
Rehren, K.-H., Schroer, B.: Einstein causality and Artin braids. Nucl. Phys.B312, 715–750 (1989)
Rehren, K.-H.: Field operators for anyons and plektons. Commun. Math. Phys.145, 123–148 (1992)
Roberts, J.E.: In preparation
Rüger, S.M.: Streutheorie für Teilchen mit Zopfgruppenstatistik. Diploma thesis, FU Berlin, 1990
Schroer, B.: Scattering properties of anyons and plektons. Presented at the “XXIV Symposion of the theory of elementary particles”, in Gosen, Berlin, 1990
Steenrod, N.: The Topology of Fiber Bundles. Princeton, NJ: Princeton University Press, 1951
Schrader, R.: Notes on Hilbert spaces with braid group statistics. Unpublished notes 1989
Tscheuschner, R.D.: Topological Spin-Statistics relation in quantum field theory. Int. J. Theor. Phys.28, 10, 1269–1310 (1989)
Wilczek, F.: Quantum Mechanics of Fractional-Spin Particles. Phys. Rev. Lett.49, 957–959 (1982)
Author information
Authors and Affiliations
Additional information
Communicated by G. Felder
Partly supported by ‘Studienstiftung des deutschen Volkes’.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02102411