Representations of the Weyl group and Wigner functions for SU(3)

Journal of Mathematical Physics

Volumn 40, Issue 7, 1999, Pages 3604-3615

  Rowe, D J ^a   Sanders, B C ^a,c   De Guise, H ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

^c MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033243807     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532911     Document Type: Article

References (40)

1. N. Ya Vilenkin, Special Functions and Theory of Group Representations, Translations of Math. Monogr. 22 (American Mathematical Society, Providence, RI, 1968); W. Miller, Lie Theory and Special Functions (Academic, New York, 1968); J. Talman, Special Functions, A Group Theoretic Approach (Benjamin, New York, 1968); H. Ui, Prog. Theor. Phys. 44, 703 (1970).
2. N. Ya Vilenkin, Special Functions and Theory of Group Representations, Translations of Math. Monogr. 22 (American Mathematical Society, Providence, RI, 1968); W. Miller, Lie Theory and Special Functions (Academic, New York, 1968); J. Talman, Special Functions, A Group Theoretic Approach (Benjamin, New York, 1968); H. Ui, Prog. Theor. Phys. 44, 703 (1970).
3. N. Ya Vilenkin, Special Functions and Theory of Group Representations, Translations of Math. Monogr. 22 (American Mathematical Society, Providence, RI, 1968); W. Miller, Lie Theory and Special Functions (Academic, New York, 1968); J. Talman, Special Functions, A Group Theoretic Approach (Benjamin, New York, 1968); H. Ui, Prog. Theor. Phys. 44, 703 (1970).
4. N. Ya Vilenkin, Special Functions and Theory of Group Representations, Translations of Math. Monogr. 22 (American Mathematical Society, Providence, RI, 1968); W. Miller, Lie Theory and Special Functions (Academic, New York, 1968); J. Talman, Special Functions, A Group Theoretic Approach (Benjamin, New York, 1968); H. Ui, Prog. Theor. Phys. 44, 703 (1970).
5. B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A 33, 4033 (1986); B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944 (1995); B. C. Sanders, G. J. Milburn, and Z. Zhang, J. Mod. Opt. 44, 1309 (1997); R. Walser, Phys. Rev. Lett. 79, 4724 (1997).
6. B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A 33, 4033 (1986); B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944 (1995); B. C. Sanders, G. J. Milburn, and Z. Zhang, J. Mod. Opt. 44, 1309 (1997); R. Walser, Phys. Rev. Lett. 79, 4724 (1997).
7. B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A 33, 4033 (1986); B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944 (1995); B. C. Sanders, G. J. Milburn, and Z. Zhang, J. Mod. Opt. 44, 1309 (1997); R. Walser, Phys. Rev. Lett. 79, 4724 (1997).
8. B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A 33, 4033 (1986); B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944 (1995); B. C. Sanders, G. J. Milburn, and Z. Zhang, J. Mod. Opt. 44, 1309 (1997); R. Walser, Phys. Rev. Lett. 79, 4724 (1997).
9. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994); B. C. Sanders and A. Mann, APS Eprint aps1998apr27_002.
10. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994); B. C. Sanders and A. Mann, APS Eprint aps1998apr27_002.
11. J. P. Draayer and S. A. Williams, Nucl. Phys. A 129, 647 (1969).
12. E. Chacón and M. Moshinsky, Phys. Lett. 23, 567 (1966); M. Moshinsky and E. Chacón, in Spectroscopic and Group Theoretic Methods in Physics (North-Holland, Amsterdam, 1968), p. 99.
13. E. Chacón and M. Moshinsky, Phys. Lett. 23, 567 (1966); M. Moshinsky and E. Chacón, in Spectroscopic and Group Theoretic Methods in Physics (North-Holland, Amsterdam, 1968), p. 99.
14. A. J. Macfarlane, E. C. G. Sudarshan, and C. Dullemond, Nuovo Cimento 30, 845 (1963).
15. N. Mukunda and L. K. Pandit, J. Math. Phys. 6, 746 (1965).
16. A. Gal and H. J. Lipkin, in Spectroscopic and Group Theoretic Methods in Physics (North-Holland, Amsterdam, 1968), p. 119.
17. R. Howe, Proc. Symposia in Pure Math. 33, 275 (1979).
18. F. D. Murnaghan, The Unitary and Rotation Groups (Spartan, Washington, DC, 1962).
19. I. M. Gel'fand and M. A. Tsetlin, Dokl. Akad. Nauk. USSR 71, 825 (1950).
20. C. R. Hagen and A. J. MacFarlane, J. Math. Phys. 6, 1355 (1965).
21. G. Benkart, Contemp. Math. 194, 1 (1996).
22. H. Weyl, Classical Groups (Princeton U.P., Princeton, NJ, 1939).
23. D. E. Littlewood, The Theory of Group Characters (Clarendon, Oxford, 1950), 2nd ed.
24. R. C. King, J. Phys. A 8, 429 (1975); G. R. E. Black, R. C. King, and B. G. Wybourne, ibid. 16, 1555 (1983); G. R. E. Black and B. G. Wybourne, ibid. 16, 2405 (1983).
25. R. C. King, J. Phys. A 8, 429 (1975); G. R. E. Black, R. C. King, and B. G. Wybourne, ibid. 16, 1555 (1983); G. R. E. Black and B. G. Wybourne, ibid. 16, 2405 (1983).
26. R. C. King, J. Phys. A 8, 429 (1975); G. R. E. Black, R. C. King, and B. G. Wybourne, ibid. 16, 1555 (1983); G. R. E. Black and B. G. Wybourne, ibid. 16, 2405 (1983).
27. M. A. Lohe and C. A. Hurst, J. Math. Phys. 12, 1882 (1971); M. Moshinsky and C. Quesne, ibid. 12, 1772 (1971); M. Kashiwara and M. Vergne, Invent. Math. 44, 1 (1978).
28. M. A. Lohe and C. A. Hurst, J. Math. Phys. 12, 1882 (1971); M. Moshinsky and C. Quesne, ibid. 12, 1772 (1971); M. Kashiwara and M. Vergne, Invent. Math. 44, 1 (1978).
29. M. A. Lohe and C. A. Hurst, J. Math. Phys. 12, 1882 (1971); M. Moshinsky and C. Quesne, ibid. 12, 1772 (1971); M. Kashiwara and M. Vergne, Invent. Math. 44, 1 (1978).
30. D. J. Rowe, B. G. Wybourne, and P. H. Butler, J. Phys. A 18, 939 (1985).
31. J. Deenen and C. Quesne, J. Phys. A 16, 2095 (1983); C. Quesne, ibid. 17, 777, 791 (1984); R. Le Blanc and D. J. Rowe, ibid. 18, 1891, 1905 (1985).
32. J. Deenen and C. Quesne, J. Phys. A 16, 2095 (1983); C. Quesne, ibid. 17, 777, 791 (1984); R. Le Blanc and D. J. Rowe, ibid. 18, 1891, 1905 (1985).
33. J. Deenen and C. Quesne, J. Phys. A 16, 2095 (1983); C. Quesne, ibid. 17, 777, 791 (1984); R. Le Blanc and D. J. Rowe, ibid. 18, 1891, 1905 (1985).
34. D. J. Rowe, Rep. Prog. Phys. 48, 1419 (1985); Prog. Part. Nucl. Phys. 37, 265 (1996).
35. D. J. Rowe, Rep. Prog. Phys. 48, 1419 (1985); Prog. Part. Nucl. Phys. 37, 265 (1996).
36. R. Brauer, Ann. Math. 38, 857 (1937).
37. A. J. Dragt, "Lectures on nonlinear orbit dynamics," in Physics of High Energy Particle Accelerators, AIP Conf. Proc. 87, 147 (1982).
38. V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U.P., Cambridge, 1984).
39. D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Going Beyond Bell's Theorem," in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989), p. 73; D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
40. D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Going Beyond Bell's Theorem," in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989), p. 73; D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).