Irreducible representations of deformed oscillator algebra and q-special functions

International Journal of Modern Physics A

Volumn 12, Issue 1, 1997, Pages 153-158

  Damaskinsky, E V ^a   Kulish, P P ^b,c  

^a Defense Constructing Engineering Institute   (Russian Federation)

^b UNIVERSITY OF VALENCIA   (Spain)

^c STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039996328     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X97000207     Document Type: Article

References (41)

1. E. P. Wigner, Phys.Rev., (1950) 77, 711.
2. H. Rampacher, H. Stumpf and F. Wagner, Fortschr. Phys., (1965) 13, 385.
3. L. O'Raifeartaigh and C. Ryan, Proc. Roy. Irish. Ac., ser.A., (1963) 62, 93;
4. B. Gruber and L. O'Raifeartaigh, Proc. Roy. Irish. Ac., ser.A., (1964) 63, 69.
5. D. D. Coon et al., Phys. Rev. D., (1970) D2, 2349;
6. Phys. Rev. D., (1972) D5, 1429.
7. M. Arik and D.D. Coon, J. Math. Phys., (1976) 17, no.4, 524.
8. L. C. Biedenharne, J. Phys. A., (1989) 22, no.18, L873.
9. A. J. Macfarlane, J. Phys. A., (1989) 22, no.21, 4581.
10. P. P. Kulish and N. Yu. Reshetikhin, Zap. Nauch. Semin. LOMI, (1981) 101, 101.
11. P. P. Kulish and E. V. Damaskinsky, J. Phys. A., (1990) 23, no.9, L415.
12. W. Pusz and S. L. Woronowicz, Repts Math. Phys., (1989) 27, no.2, 231.
13. M. Chaichian and P. P. Kulish, Phys.Lett.B., (1990) 234, no.1/2, 72; M. Chaichian and P. P. Kulish, (1990) Pr-t. CERN-TH 5969/90;
14. M. Chaichian, P. P. Kulish and J. Lukierski, Phys. Lett. B., (1991) 262, no.1, 43.
15. R. Floreanini and L. Vinet, Lett. Math. Phys., (1991) 22, no.1, 45;
16. Phys. Lett. A., (1992) 170, no.1, 21;
17. Ann. Phys., (N.Y.), (1993) 221, no.1, 53.
18. E. V. Damaskinsky and P. P. Kulish, Zap. Nauch. Semin. LOMI, (1991) 189, 37 (in Russian);
19. English transl: J. Soviet. Math., (1992) 62, 2963;
20. E. V. Damaskinsky and P. P. Kulish, Quantum groups, deformed oscillators and their interrelations, Proc. Workshop "Finite dimensional integrable systems", JINR, Dubna, July, 1994.
21. H. Exton, q-hypergeometric functions and applications, Chichester. Ellis Horwood, 1983;
22. G. Gasper, M. Rahman, Basic Hypergeometric Series, (Cambridge Univ. Press, 1990).
23. D. McAnally, J. Math. Phys., (1995) 36, no.1, 546; 574.
24. N. M. Atakishiev, J. Phys. A : Math. Gen. (1996) 29, no.10, L 223.
25. E. Damaskinsky and P. Kulish, Zap. Nauch. Sem. POMI, (1992) 199, 81 (in Russian).
26. I. M. Burban and A. U. Klymik, Lett. Math. Phys., (1993) 29, no.1, 13;
27. W.-S. Chung and A. U. Klimyk, J. Math. Phys., (1996) 37, no.2, 917.
28. N. Akhiezer, The classical moment problem, Olyver and Boyd, Edinburgh, 1985;
29. Ju. Berezanskii, Eigenfunction expansion of self-adjoint operators, Providence (R.I.), AMS, 1968.
30. M. R-Mointeiro et al., Phys. Rev. Lett., (1996) 76, no.7, 1098.
31. A. A. Andrianov et al., Phys. Lett. A., (1996) 217, 7.
32. A. Lorek, J. Wess, Z. Phys. C., (1995) 67, no.4, 671.
33. M. Yamamoto, pr-t 1996.
34. P. P. Kulish, Teor. Math. Phys., (1991) 85, no.1, 158.
35. T. L. Curtright, in T. L. Curtright, D. Fairlie and C. K. Zachos (Eds.), Quantum Groups, Proceedings of the Argonne Workshop (World Scientific, Singapore, 1990).
36. J. Kariel and C. Quesne, J. Math. Phys., (1996) 37, no.4, 1650.
37. R. Chakrabarti and R. Jagannatham, (1991) J. Phys. A., 24, no.13, L 711.
38. V. V. Borsov et al., Stockholm pr-t, TRITA-MAT-1995-MA-20; q-alg 9509022.
39. A. J. Bracken et al., J. Phys. A., (1991) 24, no.7, 1379.
40. P. P. Kulish, Irreducible representations of deformed oscillator and coherent states, Preprint KTH-96/11, 11pp., Stockholm 1996.
41. A. M. Perelomov, Helv. Phys. Acta, (1996) 68, 554.