We review the appearance of the braid group in statistical physics. In particular, we explain its relevance to the anyon model of fractional statistics and conformal field theory.
@article{bwmeta1.element.bwnjournal-article-bcpv42i1p221bwm,
author = {McCabe, J. and Wydro, T.},
title = {Topics in statistical physics involving braids},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {221-234},
zbl = {0905.20025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p221bwm}
}
McCabe, J.; Wydro, T. Topics in statistical physics involving braids. Banach Center Publications, Tome 43 (1998) pp. 221-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p221bwm/
[000] [1] J. M. Leinaas and J. Myhreim, Il Nuovo Cimento 37B (1977) 1.
[001] [2] Y.-S. Wu, Phys. Rev. Lett. 52 (1984) 2103; J. Birman, Links, Braids and Mapping Class Groups (Princeton University Press 1974).
[002] [3] D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251 (1985) 117.
[003] [4] for a review see: F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific 1990); A. Comtet, J. McCabe, and S. Ouvry, Images de la Physique (1992) 21.
[004] [5] see generally: M. Sporre, J. J. Verbaarshot, and I. Zahed, Phys. Rev. Lett. 67 (1991) 1817; G. V. Dunne, A. Lerda, and C. A. Trugenberger, Int. J. of Mod. Phys. B5 (1991) 1675; ibid Nucl. Phys. B370 (1992) 601; A. Khare, J. McCabe, and S. Ouvry, Phys. Rev. D46 (1992) 2714.
[005] [6] R. B. Laughlin, Phys. Rev. Lett. 60 (1988) 2677; Y.-H. Chen, F. Wilczek, E. Witten, and B. I. Halperin, Int. J. of Mod. Phys. B3 (1989) 1001.
[006] [7] A. M. Polyakov, JETP Lett. 12 (1970) 381.
[007] [8] A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B241 (1984) 333; for a review see articles of P. Ginsparg and J. Cardy in Les Houches Summer School 1988 (Eds. E. Brezin and J. Zinn-Justin).
[008] [9] D. Friedan, Z. Qiu, and S. Shenker, Phys. Rev. Lett. 52 (1984) 1575.
[009] [10] Vl. S. Dotsenko and V. Fateev, Nucl. Phys. B240 (1984) 312; ibid, B251 (1985) 691; Vl. Dotsenko, Nucl. Phys. B235 (1984) 54; J. McCabe and T. Wydro, ENSLAPP-L-526/95 (cond-mat/9507033).
[010] [11] G. Von Gehlen, V. Rittenberg, and T. Vescan, J. of Physics A20 (1987) 2577; G. T. Barkema and J. McCabe, J. Stat. Phys. 84 (1996) 1067.
[011] [12] V. Kac, Lecture Notes in Physics 94 (Springer 1979).
[012] [13] G. Moore and N. Seiberg, Phys. Lett. 212B (1988) 451; also in Superstrings 1989 (Eds. M. Green, R. Iengo, S. Randjbar-Daemi, E. Sezgin, and A. Strominger) 1.
[013] [14] L. Alvarez-Gaume, C. Gomez, and G. Sierra, in Physics and Mathematics of Strings (Eds. L. Brink, D. Friedan, and A.M. Polyakov) 16. | Zbl 0689.17009