Deforming maps for Lie group covariant creation and annihilation operators

Journal of Mathematical Physics

Volumn 39, Issue 6, 1998, Pages 3437-3452

  Fiore, Gaetano ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032379630     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532439     Document Type: Article

References (36)

1. E. Abe, Hopf Algebras, Cambridge Tracts in Mathematics 74 (Cambridge U.P., Cambridge, 1980).
2. V. G. Drinfeld, "Quantum Groups," edited by A. Gleason, in Proceedings of the International Congress of Mathematicians, Berkeley, 1986 (American Mathematical Society, Providence, 1987), Vol. 1, p. 798.
3. W. Pusz and S. L. Woronowicz, Rep. Math. Phys. 27, 231 (1989).
4. J. Wess and B. Zumino, Nucl. Phys. B, Proc. Suppl. 18, 302 (1991).
5. L. C. Biedenharn, J. Phys. A 22, L873 (1989); A. J. Macfarlane, J. Phys. A 22, 4581 (1989).
6. L. C. Biedenharn, J. Phys. A 22, L873 (1989); A. J. Macfarlane, J. Phys. A 22, 4581 (1989).
7. S. Vokos and C. Zachos, Mod. Phys. Lett. A 9, 1 (1994) and references therein; see also J. Seifert, Ph.D. thesis, Munich University (1996) (in German).
8. S. Vokos and C. Zachos, Mod. Phys. Lett. A 9, 1 (1994) and references therein; see also J. Seifert, Ph.D. thesis, Munich University (1996) (in German).
9. T. L. Curtright and C. K. Zachos, Phys. Lett. B 243, 237 (1990).
10. T. L. Curtright, G. I. Ghandour, and C. K. Zachos, J. Math. Phys. 32, 676 (1991).
11. G. Fiore, "Drinfel'd Twist and q-deforming Maps for Lie Groups Covariant Heisenberg Algebras," Preprint LMU-TPW 97-07 and e-print q-alg/9708017.
12. M. Gerstenhaber, Ann. Math. 79, 59 (1964).
13. F. du Cloux, Asterisque (Soc. Math. France) 124-125, 129 (1985).
14. M. Pillin, Commun. Math. Phys. 180, 23 (1996).
15. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Stemheimer, Ann. Phys. (N.Y.) 111, 61 (1978); 111, 111 (1978).
16. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Stemheimer, Ann. Phys. (N.Y.) 111, 61 (1978); 111, 111 (1978).
17. V. G. Drinfeld, Dokl. Akad. Nauk SSSR 273, 531 (1983); Translation: Soviet Math. Dokl. 28, (1983).
18. V. G. Drinfeld, Dokl. Akad. Nauk SSSR 273, 531 (1983); Translation: Soviet Math. Dokl. 28, (1983).
19. N. Yu. Reshetikhin Lett. Math. Phys. 20, 331 (1990).
20. V. G. Drinfeld, Leningrad Math. J. 1, 1419 (1990).
21. O. Ogievetsky, Lett. Math. Phys. 24, 245 (1992).
22. G. Fiore and P. Schupp, Nucl. Phys. B 470, 211 (1996); "Statistics and Quantum Group Symmetries, e-print hep-th/ 9605133, Banach Center Publications, Vol. 40, Inst. of Mathematics, Polish Academy of Sciences, Warszawa, edited by P. Budzyski, W. Pusz, and S. Zakrweski.
23. G. Fiore and P. Schupp, Nucl. Phys. B 470, 211 (1996); "Statistics and Quantum Group Symmetries, e-print hep-th/ 9605133, Banach Center Publications, Vol. 40, Inst. of Mathematics, Polish Academy of Sciences, Warszawa, edited by P. Budzyski, W. Pusz, and S. Zakrweski.
24. G. Fiore, "On Bose-Fermi Statistics, Quantum Group Symmetry, and Second Quantization," Preprint LMU-TPW 96-17 and e-print hep-th/9611144. To appear in the proceedings of "Group21."
25. C. Ohn, Lett. Math. Phys. 166, 63 (1994).
26. L. D. Faddeev, N. Y. Reshetikhin, and L. A. Takhtajan, Algebra i Analysis 1, 178 (1989); translation: Leningrad Math. J. 1, 193 (1990).
27. L. D. Faddeev, N. Y. Reshetikhin, and L. A. Takhtajan, Algebra i Analysis 1, 178 (1989); translation: Leningrad Math. J. 1, 193 (1990).
28. B. Jurco, Commun. Math. Phys. 166, 63 (1994).
29. See, e.g., L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics, Encyclopedia of Mathematics and its Applications, Vol. 8 (Addison-Wesley Reading, MA, 1981); V. Manko, G. Marmo, P. Vitale, and F. Zaccaria, Int. J. Mod. Phys. A 9, 5541 (1994).
30. See, e.g., L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics, Encyclopedia of Mathematics and its Applications, Vol. 8 (Addison-Wesley Reading, MA, 1981); V. Manko, G. Marmo, P. Vitale, and F. Zaccaria, Int. J. Mod. Phys. A 9, 5541 (1994).
31. W. Pusz, Rep. Math. Phys. 27, 349 (1989).
32. S. Majid, Foundations of Quantum Groups (Cambridge U.P., Cambridge, 1995).
33. T. Hayashi, Commun. Math. Phys. 127, 129 (1990).
34. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, Vol. 35 (Cambridge U.P., Cambridge, 1990).
35. See, for instance, A. Lorek, A. Ruffing, and J. Wess, "A q-deformation of the Harmonic Oscillator," preprint MPI-PHT-96-26 and e-print hep-th/9605161, and references therein.
36. A. Kempf, J. Math. Phys. 35, 4483 (1994).