Polynomial Lie algebras and associated pseudogroup structures in composite quantum models

Reports on Mathematical Physics

Volumn 40, Issue 2, 1997, Pages 235-244

  Karassiov, Valery P ^a  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031256297     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0034-4877(97)85920-4     Document Type: Article

References (27)

1. [1] H. Weyl: The Theory of Groups and Quantum Mechanics, Dover Publ., N. Y. 1950; H. Weyl: The Classical Groups, Princeton University Press, Princeton 1939.
2. [1] H. Weyl: The Theory of Groups and Quantum Mechanics, Dover Publ., N. Y. 1950; H. Weyl: The Classical Groups, Princeton University Press, Princeton 1939.
3. [2] A. O. Barut and R. Ra̧czka: Theory of Groups Representations and Applications, PWN, Warszawa 1977.
4. [3] Y. Ohnuki and S. Kamefuchi: Quantum Field Theory and Parastatistics, University Press, Tokyo 1982.
5. [4] A. M. Perelomov: Generalized Coherent States and Their Applications, Springer, Berlin 1986.
6. [5] V. P. Karassiov: J. Phys. A 25 (1992), 393; V. P. Karassiov: Deformations of Lie (Super)algebras in Quantum Theories with Internal Symmetries, Preprint FIAN No 65 of Lebedev Institute, Moscow (1992); V. P. Karassiov, Trudy FIAN 208 (1992), 18.
7. [5] V. P. Karassiov: J. Phys. A 25 (1992), 393; V. P. Karassiov: Deformations of Lie (Super)algebras in Quantum Theories with Internal Symmetries, Preprint FIAN No 65 of Lebedev Institute, Moscow (1992); V. P. Karassiov, Trudy FIAN 208 (1992), 18.
8. [5] V. P. Karassiov: J. Phys. A 25 (1992), 393; V. P. Karassiov: Deformations of Lie (Super)algebras in Quantum Theories with Internal Symmetries, Preprint FIAN No 65 of Lebedev Institute, Moscow (1992); V. P. Karassiov, Trudy FIAN 208 (1992), 18.
9. [6] A. Odzijewicz: Commun. Math. Phys. 150 (1992), 385; A. Odzijewicz: Quantum Algebras and q-Special Functions Related to Coherent States Maps of the Disc, Preprint IFT 18/95 of Warsaw University 1995.
10. [6] A. Odzijewicz: Commun. Math. Phys. 150 (1992), 385; A. Odzijewicz: Quantum Algebras and q-Special Functions Related to Coherent States Maps of the Disc, Preprint IFT 18/95 of Warsaw University 1995.
11. [7] S. M. Khoroshkin and V. N. Tolstoy: Commun. Math. Phys. 141 (1991), 599.
12. [8] V. G. Kac: Infinite Dimensional Lie Algebras, Cambridge University Press, Cambridge 1990.
13. [9] S. L. Woronowicz: Commun. Math. Phys. 111 (1987), 613.
14. [10] H.-D. Doebner and V. K. Dobrev, eds.: Quantum Symmetries, World Scientific, Singapore 1993; Adv. Appl. Clifford Algebras 4, No S1 [special issue] (1994).
15. [10] H.-D. Doebner and V. K. Dobrev, eds.: Quantum Symmetries, World Scientific, Singapore 1993; Adv. Appl. Clifford Algebras 4, No S1 [special issue] (1994).
16. [11] M. Rocek: Phys. Lett. B 255 (1991), 554.
17. [12] V. P. Karassiov: Teor. Mat. Fiz. 95 (1993), 3; V. P. Karassiov: J. Phys. A 27 (1994), 153; V. P. Karassiov and A. B. Klimov: Phys. Lett. A 189 (1994), 43.
18. [12] V. P. Karassiov: Teor. Mat. Fiz. 95 (1993), 3; V. P. Karassiov: J. Phys. A 27 (1994), 153; V. P. Karassiov and A. B. Klimov: Phys. Lett. A 189 (1994), 43.
19. [12] V. P. Karassiov: Teor. Mat. Fiz. 95 (1993), 3; V. P. Karassiov: J. Phys. A 27 (1994), 153; V. P. Karassiov and A. B. Klimov: Phys. Lett. A 189 (1994), 43.
20. pd(2) in action: smooth sl(2) mappings and approximations, in Symmetry Methods in Physics, vol. 1, eds. N. A. Sissakian and G. S. Pogosyan, JINR Publ. Dep., Dubna 1996.
21. [14] P. Jordan: Zeit. Phys. 94 (1935), 531; T. Holstein and H. Primakoff: Phys. Rev. 58 (1940), 1098.
22. [14] P. Jordan: Zeit. Phys. 94 (1935), 531; T. Holstein and H. Primakoff: Phys. Rev. 58 (1940), 1098.
23. [15] M. Moshinsky and C. Quesne: J. Math. Phys. 12 (1971), 1772.
24. [16] R. Howe: Proc. Symp. Pure Math. AMS 33, part 2 (1979), 275.
25. [17] M. Gaudin: La Fonction d'Onde de Bethe, Masson, Paris 1987.
26. [18] R. A. Brandt and O. W. Greenberg: J. Math. Phys. 10 (1969), 1168.
27. [19] F. Olver: Asymptotics and Special Functions, Academic Press, New York 1974.