Scattering theory for plektons in 2 + 1 dimensions
Annales de l'I.H.P. Physique théorique, Volume 64 (1996) no. 4, p. 523-541
@article{AIHPA_1996__64_4_523_0,
     author = {Fredenhagen, Klaus and Gaberdiel, M. R.},
     title = {Scattering theory for plektons in 2 + 1 dimensions},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {64},
     number = {4},
     year = {1996},
     pages = {523-541},
     zbl = {0860.47050},
     mrnumber = {1407759},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1996__64_4_523_0}
}
Fredenhagen, K.; Gaberdiel, M. R. Scattering theory for plektons in 2 + 1 dimensions. Annales de l'I.H.P. Physique théorique, Volume 64 (1996) no. 4, pp. 523-541. http://www.numdam.org/item/AIHPA_1996__64_4_523_0/

[1] Artin E.. In: LANG S. and TATE J. E. Eds. The collected papers of E. ARTIN. Addison-Wesley, 1965. | MR 176888

[2] Buchholz D. and Fredenhagen K., Locality and the structure of particle states. Commun. Math. Phys., Vol. 84, 1982, pp. 1-54. | MR 660538 | Zbl 0498.46061

[3] Doplicher S., Haag, R. and Roberts J.E., Local Observables and particle statistics I + II. Commun. Math. Phys., Vol. 23, 1971, pp. 199-230 and Vol. 35, 1974, pp. 49-85. | MR 297259

[4] Doplicher S. and Roberts J.E., Why there is a Field Algebra with a Compact Gauge Group Describing the Superselection Structure in Particle Physics, Commun. Math. Phys., Vol. 131, 1990, pp. 51-107. | MR 1062748 | Zbl 0734.46042

[5] Ferrari F., Conformal field theories with nonabelian symmetry group. Phys. Lett., Vol. B277, 1992, pp. 423-434, Ferrari F.., Multivalued fields on the complex plane and braid group statistics. Int. Journ. Mod. Phys., Vol. A9, 1994, pp. 313-326. | MR 1154744 | Zbl 0985.81694

[6] Fredenhagen K., On the existence of antiparticles, Commun. Math. Phys., Vol. 79, 1981, pp. 141-151. | MR 609233

[7] Fredenhagen K., Sum rules for spins in (2 + 1)-dimensional quantum field theory. In: DOEBNER H. D. and HENNIG J. Eds. Quantum Groups. Proceedings, Quantum Group Workshop Clausthal 1989. Lecture Notes in Physics, Vol. 370, pp. 340-348, Springer 1990. | MR 1201836 | Zbl 0724.53053

[8] Fredenhagen K., Generalizations of the theory of superselection sectors. In: KASTLER Ed, The Algebraic Theory of Superselection Sectors, pp. 379-387. World Scientific 1990. | MR 1147469

[9] Fredenhagen K., Structure of Superselection Sectors in Low Dimensional Quantum Field Theory. In: CHAU L. L. and NAHM W. Eds., Differential Geometric Methods in Theoretical Physics. Plenum Press 1990. | MR 1169477

[10] Fredenhagen K., Global observables in local quantum physics. In: ARAKI H. et al. Eds., Quantum and Non-Commutative Analysis, pp. 41-51. Kluwer 1993. | MR 1276280 | Zbl 0847.46043

[11] Fredenhagen K. and Gaberdiel, M.R.: in preparation.

[12] Fredenhagen K., Gaberdiel M.R. and Rüger S.M., Scattering States of Plektons (Particles with Braid Group Statistics) in 2 + 1 Dimensional Quantum Field Theory. DAMTP-94-90, to appear in Commun. Math. Phys. | MR 1370098 | Zbl 0851.46050

[13] Fredenhagen K., Rehren K.-H.. and Schroer B., Superselection sectors with braid group statistics and exchange algebras. I: General theory, II: Geometric aspects and conformal covariance. Commun. Math. Phys., Vol. 125, 1989, pp. 201-226 and Rev. Math. Phys., Special Issue, 1992, pp. 113-157. | MR 1016869 | Zbl 0682.46051

[14] Fröhlich J. and Gabbiani F., Braid Statistics in Local Quantum Field Theory, Rev. Math.. Phys., Vol. 2, 1990, pp. 251. | MR 1104414 | Zbl 0723.57002

[15] Fröhlich J. and Marchetti P.A., Spin-statistics theorem and scattering in planar quantum field theories with braid statistics. Nucl. Phys., Vol. B356, 1991, pp. 533-573. | MR 1115846

[16] Guido D. and Longo R., Relativistic invariance and large conjugation in quantum field theory. Commun. Math. Phys., Vol. 148, 1992, pp. 521-551. | MR 1181069 | Zbl 0771.46039

[17] Haag R., Quantum field theories with composite particles and asymptotic completeness. Phys. Rev., Vol. 112, 1958, pp. 669-673; Ruelle D., On the asymptotic condition in quantum field theory. Helv. Phys. Acta, Vol. 35, 1962, pp. 147-163. | MR 99859

[18] Haag R., Local Quantum Physics. Springer 1992. | MR 1182152 | Zbl 0777.46037

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

[20] Leinaas J.M., Myrheim J., On the theory of identical particles. Il Nuovo Cimento, Vol. 37B, 1977, pp. 1-23.

[21] Longo R., Index of subfactors and statistics of quantum fields I + II. Commun. Math. Phys., Vol. 126, 1989, pp. 217-247 and Vol. 130, 1990, pp. 285-309. | MR 1027496 | Zbl 0682.46045

[22] Mack G. and Schomerus V., Conformal field algebras with quantum symmetry from the theory of superselection sectors, Commun. Math. Phys., Vol. 134, 1990, pp. 139-196. | MR 1079804 | Zbl 0715.17028

[23] Mund J. and Schrader R., Hilbert spaces for nonrelativistic and relativistic 'Free' Plektons (particles with braid group statistics). SFB 288 Preprint No. 74, 1993.

[24] Reed M. and Simon B., Methods of modem mathematical physics. III Scattering Theory. Academic Press 1979. | MR 529429 | Zbl 0405.47007

[25] Rehren K.-H. and Schroer B., Einstein causality and Artin braids. Nucl. Phys., Vol. B312, 1989, pp. 715-750. | MR 980192

[26] Rehren K.-H., Field operators for anyons and plektons, Commun. Math. Phys., Vol. 145, 1992, pp. 123-148. | MR 1155286 | Zbl 0766.46047

[27] Roberts J.E., The Statistical Dimension, Conjugation and the Jones Index. To appear in Rev. Math. Phys. | MR 1332981 | Zbl 0836.46056

[28] Schroer B., Scattering properties of anyons and plektons. Presented at the "XXIV Symposium of the theory of elementary particles" in Gosen, Berlin, 1990.

[29] Steenrod N., The Topology of Fiber Bundles, Princeton University Press, 1951. | Zbl 0054.07103

[30] Schrader R., Notes on Hilbert spaces with braid group statistics. (Unpublished notes 1989).

[31] Tscheuschner R.D., Topological Spin-Statistics relation in quantum field theory. Int. Journ. Theor. Phys., Vol. 28, 10, 1989, pp. 1269-1310. | MR 1031608 | Zbl 0737.58070

[32] Wilczek F., Quantum Mechanics of Fractional-Spin Particles, Phys. Rev. Lett., Vol. 49, 1982, pp. 957-959. | MR 675053