Abstract
In recent years there has been an intense interest in the theory of anyons, particles obeying fractional statistics in 1 + 2 dimensions[1]. This is so not only because the theory itself exhibits very interesting mathematical structures, but also because it could be of relevance to some condensed matter systems, notably the fractional quantum Hall effect [2] and the high T c , superconductivity[3].
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References
J.M. Leinaas and J. Myrheim, Nuovo Cimento 37B (1977) 1;
G.A. Goldin, R. Menikoff, and D.H. Sharp, J. Math. Phys. 22 (1981) 1664; F. Wilczek, Phys. Rev. Lett. 48 (1982) 1144; ibid. 49 (1982) 957.
R.B. Laughlin, Phys. Rev. Lett. 50 (1983) 1395;
B.I. Halperin, Phys. Rev. Lett. 52 (1984) 1583;
D. Arovas, R. Schrieffer and F. Wilczek, Phys. Rev. Lett. 53 (1984) 722; R. Tao and Y-S. Wu, Phys. Rev. B31 (1985) 6859.
V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett. 59 (1987) 2095; R. B. Laughlin, Science 242 (1988) 525;
R. B. Laughlin, Phys. Rev. Lett. 60 (1988) 2677.
J. Schonfeld, Nucl. Phys. B185 (1981) 157;
R. Jackiw and S. Templeton, Phys. Rev. D23 (1981) 2291;
S. Deser, R. Jackiw, and S. Templeton, Phys. Rev. Lett. 48 (1982) 975; Ann. Phys. (N.Y.) 140 (1982) 372; 185 (1988) 406 (E);
C.R. Hagen, Ann. Phys. (N. Y.) 157 (1984) 342; Phys. Rev. D31 (1985) 2135.
Y. Hosotani, Phys. Rev. Lett. 62 (1989) 2785; Phys. Rev. Lett. 64 (1990) 1691.
D.J. Thouless and Y.S. Wu, Phys. Rev. B31 (1985) 1191;
K. Lee, Boston Univ. report, Anyons on spheres and tori,BU/HEP-89–28;
A.P. Polychronakos, Ann. Phys. (N. Y.) 203 (1990) 231; Univ. of Florida preprint, Abelian Chern-Simons theories and conformal blocks UFIFT-HEP89–9; Phys. Lett. 241B (1990) 37;
A. Comtet, J. McCabe and S. Ouvry, IPN preprint, Some remarks on anyons on the 2-sphere (to appear in Phys. Rev. D (1992).
S. Elitzur, G. Moore, A. Schwimmer and N. Seiberg, Nucl. Phys. B326 (1989) 108;
M. Bos and V.P. Nair, Phys. Lett. 223B (1989) 61; Int. J. Mod. Phys. A5 (1990) 959;
J.M.F. Labastida and A.V. Ramallo, Phys. Lett. 227B (1989) 92; Phys. Lett. 228B (1989) 214;
H. Murayama, Z. Phys. C48 (1990) 79.
E. Witten, Comm. Math. Phys. 121 (1989) 351.
E. Fradkin, Phys. Rev. Lett,. 63 (1989) 322.
T. Einarsson, Phys. Rev. Lett. 64 (1990) 1995; Göteberg preprint, Fractional statistics on compact surfaces, ITP-91–1 (1991).
G.C. Segre, Pennsylvania preprint, A model of superconductivity.
S. Randjbar-Daemi, A. Salarn, and J. Strathdee, Phys. Lett. 240B (1990) 121.
R. Iengo and K. Lechner, Nucl. Phys. B346 (1990) 551; Nucl. Phys. B364 (1991) 551.
G. Cristofano, G. Maiella, R. Musto and F. Nicodemi, Phys. Lett. 262B (1991) 88; Mod. Phys. Lett. A6 (1991) 1779.
X.G. Wen, E. Dagotto, and E. Fradkin, Phys. Rev. B42 (1990) 6110.
S. Chakravarty and Y. Hosotani, Phys. Rev. D44 (1991) 441.
T.D. Imbo and J. March-Russell, Phys. Lett. 252B (1990) 84.
Y.S. Wu, Y. Hatsugai, and M. Kohmoto, Phys. Rev. Lett. 66 (1991) 659; Phys. Rev. B43 (1991) 2661.
C.-L. Ho and Y. Hosotani, Int. J. Mod. Phys. A7 (1992) 5797.
C.-L. Ho and Y. Hosotani, Minnesota preprint, Operator Algebra in ChernSimons Theory on a Torus,TPI-MINN-92/41-T (Sep 92).
E. Witten, Nucl. Phys. B258 (1985) 75; Y. Hosotani, Ann. Phys. (N.Y.) 190 (1989) 233.
G.Date, T.R. Govindarajan, P. Sankaran and R. Shankar, Comm. Math. Phys. 132 (1990) 293.
X.G. Wen, Phys. Rev. B40 (1989) 7387; Int. J. Mod. Phys. B4 (1990) 239.
K. Lechner, Trieste ISAS preprint, Anyon physics on the torus,thesis, (Apr. 91).
J.S. Birman, Comm. Pure and Applied Math. 22 (1969) 41.
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Ho, CL., Hosotani, Y. (1994). Braid Group Structure in Chern-Simons Theory on a Torus. In: Goeke, K., Hwang, WY.P., Speth, J. (eds) Contemporary Topics in Medium Energy Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9835-7_25
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