Topological and algebraic aspects of quantization : symmetries and statistics
Annales de l'I.H.P. Physique théorique, Volume 49 (1988) no. 3, p. 387-396
@article{AIHPA_1988__49_3_387_0,
     author = {Sudarshan, E. C. G. and Imbo, Tom D. and Imbo, Chandni Shah},
     title = {Topological and algebraic aspects of quantization : symmetries and statistics},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {3},
     year = {1988},
     pages = {387-396},
     mrnumber = {988435},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1988__49_3_387_0}
}
Sudarshan, E. C. G.; Imbo, Tom D.; Imbo, Chandni Shah. Topological and algebraic aspects of quantization : symmetries and statistics. Annales de l'I.H.P. Physique théorique, Volume 49 (1988) no. 3, pp. 387-396. http://www.numdam.org/item/AIHPA_1988__49_3_387_0/

[2] C.J. Isham, in Relativity, Groups and Topology II, edited by B. S. DeWitt and R. Stora (Elsevier, New York, 1984), and references therein.

[5] T.D. Imbo, C. Shah Imbo and E.C.G. Sudarshan, Center for Particle Theory. Report, No. DOE-ER40200-142, 1988.

[7] B. Kostant, in Lecture Notes in Mathematics, vol. 170 (Springer Verlag, Berlin, 1970).

[8] M.G.G. Laidlaw and C.M. Dewitt, Phys. Rev., t. D 3, 1971, p. 1375 ; M.G.G. Laidlaw, Ph. D. Thesis, University of North Carolina, 1971.

[9] E.C.G. Sudarshan, T.D. Imbo and T.R. Govindarajan, Phys. Lett., t. B 213, 1988, p. 471. | MR 967734

[10] T.D. Imbo and E.C.G. Sudarshan, Phys. Rev. Lett., t. 60, 1988, p. 481. | MR 925746

[11] A group G is called perfect if [G, G] = G where [G, G] is the commutator (or derived) subgroup of G. See, for example, D.J.S. Robinson, A Course in the Theory of Groups (Springer Verlag, New York, 1982). | Zbl 0483.20001

[12] E. Fadell and L. Neuwirth, Math. Scand., t. 10, 1962, p. 111. | MR 141126 | Zbl 0136.44104

[13] R. Fox and L. Neuwirth, Math. Scand., t. 10, 1962, p. 119 ; J.S. Birman, Braids, Links and Mapping Class Groups (Princeton University Press, Princeton, 1974), and references therein. | MR 150755 | Zbl 0117.41101

[14] T.D. Imbo and C. Shah Imbo, Center for Particle Theory. Report, in preparation.

[15] Y.-S. Wu, Phys. Rev. Lett., t. 52, 1984, p. 2103. | MR 746736

[16] D.J. Thouless and Y.-S. Wu, Phys. Rev., t. B 31, 1985, p. 1191.

[17] J.S. Dowker, J. Phys., t. A 18, 1985, p. 3521. | MR 822912 | Zbl 0592.60095

[18] J.S. Lomont, Applications of Finite Groups (Academic Press, New York, 1959). | MR 102552 | Zbl 0085.25403

[19] F.J. Bloore, I. Bratley and J.M. Selig, J. Phys., t. A 16, 1983, p. 729 ; R.D. Sorkin, in Topological Properties and Global Structure of Space-Time, edited by P. G. Bergmann and V. de Sabbata (Plenum, New York, 1986); H.S. Green, Phys. Rev., t. 90, 1953, p. 270. | MR 706191

[20] E. Artin, Abh. Math. Sem. Hamburg, t. 4, 1926, p. 47. | JFM 51.0450.01

[21] B3(R2) is torsion-free and is also isomorphic to the group of the trefoil knot. For more on braids and knots see D.L. Johnson, Topics in the Theory of Group Presentations (Cambridge University Press, Cambridge, 1980), and J. S. BIRMAN in Ref. 13. | Zbl 0437.20026

[22] J.A.H. Shepperd, Proc. Roy. Soc. London, t. A 265, 1962, p. 229. | MR 133125 | Zbl 0103.39504

[23] A.H. Clifford, Ann. Math., t. 38, 1937, p. 533. | JFM 63.0076.04 | Zbl 0017.29705

[24] E. Fadell and J. Van Buskirk, Duke Math. Jour, t. 29, 1962, p. 243 ; J. Van Buskirk, Trans. Amer. Math. Soc., t. 122, 1966, p. 81. | MR 141128 | Zbl 0122.17804

[25] See Refs. 7 and 8, as well as D. Finkelstein, J. Math. Phys., t. 7, 1966, p. 1218 ; D. Finkelstein and J. Rubinstein, J. Math. Phys., t. 9, 1968, p. 1762; L.S. Schulman, Phys. Rev., t. 176, 1968, p. 1558 ; J. Math. Phys., t. 12, 1971, p. 304; J.S. Dowker, J. Phys., t. A 5, 1972, p. 936.

[26] Further references on nonscalar quantizations are, A.P. Balachandran, Nucl. Phys., t. B 271, 1986, p. 227; Syracuse University Report No. SU-4428-361, 1987 ; Syracuse University Report No. SU-4428-373, 1988 ; as well as Ref. 2.