Topological and algebraic aspects of quantization : symmetries and statistics

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1. [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. 
2. [5] T.D. Imbo, C. Shah Imbo and E.C.G. Sudarshan, Center for Particle Theory. Report, No. DOE-ER40200-142, 1988. 
3. [7] B. Kostant, in Lecture Notes in Mathematics, vol. 170 (Springer Verlag, Berlin, 1970). 
4. [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. 
5. [9] E.C.G. Sudarshan, T.D. Imbo and T.R. Govindarajan, Phys. Lett., t. B 213, 1988, p. 471. MR967734
6. [10] T.D. Imbo and E.C.G. Sudarshan, Phys. Rev. Lett., t. 60, 1988, p. 481. MR925746
7. [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). Zbl0483.20001
8. [12] E. Fadell and L. Neuwirth, Math. Scand., t. 10, 1962, p. 111. Zbl0136.44104MR141126
9. [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. Zbl0117.41101MR150755
10. [14] T.D. Imbo and C. Shah Imbo, Center for Particle Theory. Report, in preparation. 
11. [15] Y.-S. Wu, Phys. Rev. Lett., t. 52, 1984, p. 2103. MR746736
12. [16] D.J. Thouless and Y.-S. Wu, Phys. Rev., t. B 31, 1985, p. 1191. 
13. [17] J.S. Dowker, J. Phys., t. A 18, 1985, p. 3521. Zbl0592.60095MR822912
14. [18] J.S. Lomont, Applications of Finite Groups (Academic Press, New York, 1959). Zbl0085.25403MR102552
15. [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. MR706191
16. [20] E. Artin, Abh. Math. Sem. Hamburg, t. 4, 1926, p. 47. JFM51.0450.01
17. [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. Zbl0437.20026
18. [22] J.A.H. Shepperd, Proc. Roy. Soc. London, t. A 265, 1962, p. 229. Zbl0103.39504MR133125
19. [23] A.H. Clifford, Ann. Math., t. 38, 1937, p. 533. Zbl0017.29705JFM63.0076.04
20. [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. Zbl0122.17804MR141128
21. [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. 
22. [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. 

1. Cécile Dewitt-Morette, Des ponts