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.
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     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},
     pages = {387--396},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {3},
     year = {1988},
     mrnumber = {988435},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1988__49_3_387_0/}
}
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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://archive.numdam.org/item/AIHPA_1988__49_3_387_0/

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[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

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

[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

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

[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 | Zbl

[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

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

[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

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

[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

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[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.