Collect. Czech. Chem. Commun. 2005, 70, 771-796
https://doi.org/10.1135/cccc20050771

Representation Theory and Wigner-Racah Algebra of the SU(2) Group in a Noncanonical Basis

Maurice R. Kibler

Institut de Physique Nucléaire de Lyon, IN2P3-CNRS et Université Claude Bernard Lyon 1, 43 bd du 11 novembre 1918, 69622 Villeurbanne Cedex, France

References

1a. Čížek J., Paldus J.: Int. J. Quantum Chem. 1977, 12, 875. <https://doi.org/10.1002/qua.560120510>
1b. Čížek J., Adams B. G., Paldus J.: Phys. Scr. 1980, 21, 364. <https://doi.org/10.1088/0031-8949/21/3-4/021>
2a. Kibler M., Négadi T.: Lett. Nuovo Cimento 1983, 37, 225. <https://doi.org/10.1007/BF02751180>
2b. Kibler M., Négadi T.: J. Phys. A: Math. Gen. 1983, 16, 4265. <https://doi.org/10.1088/0305-4470/16/18/027>
2c. Kibler M., Négadi T.: Phys. Rev. A: At., Mol., Opt. Phys. 1984, 29, 2891. <https://doi.org/10.1103/PhysRevA.29.2891>
2d. Kibler M. R.: J. Mol. Phys. 2004, 102, 1221. <https://doi.org/10.1080/00268970410001728690>
3a. Paldus J., Čížek J., Shavitt I.: Phys. Rev. A: At., Mol., Opt. Phys. 1972, 5, 50. <https://doi.org/10.1103/PhysRevA.5.50>
3b. Paldus J.: J. Chem. Phys. 1974, 57, 638. <https://doi.org/10.1063/1.1678296>
3c. Paldus J.: J. Chem. Phys. 1974, 61, 5321. <https://doi.org/10.1063/1.1681883>
3d. Paldus J.: Int. J. Quantum Chem., Quantum Chem. Symp. 1975, 9, 165. <https://doi.org/10.1002/qua.560090823>
3e. Paldus J., Čížek J.: Adv. Quantum Chem. 1975, 9, 105. <https://doi.org/10.1016/S0065-3276(08)60040-4>
3f. Paldus J.: Phys. Rev. A: At., Mol., Opt. Phys. 1976, 14, 1620. <https://doi.org/10.1103/PhysRevA.14.1620>
3g. Paldus J.: J. Chem. Phys. 1977, 67, 303. <https://doi.org/10.1063/1.434526>
3h. Paldus J., Adams B. G., Čížek J.: Int. J. Quantum Chem. 1977, 11, 813. <https://doi.org/10.1002/qua.560110511>
3i. Adams B. G., Paldus J., Čížek J.: Int. J. Quantum Chem. 1977, 11, 849. <https://doi.org/10.1002/qua.560110512>
3j. Paldus J., Čížek J., Saute M., Laforgue A.: Phys. Rev. A: At., Mol., Opt. Phys. 1978, 17, 805. <https://doi.org/10.1103/PhysRevA.17.805>
3k. Wormer P. E. S., Paldus J.: Int. J. Quantum Chem. 1979, 16, 1307. <https://doi.org/10.1002/qua.560160610>
3l. Paldus J., Wormer P. E. S.: Int. J. Quantum Chem. 1979, 16, 1321. <https://doi.org/10.1002/qua.560160611>
3m. Wormer P. E. S., Paldus J.: Int. J. Quantum Chem. 1980, 18, 841. <https://doi.org/10.1002/qua.560180317>
3n. Paldus J., Boyle M. J.: Int. J. Quantum Chem. 1982, 22, 1281. <https://doi.org/10.1002/qua.560220611>
3o. Paldus J., Takahashi M., Cho R. W. H.: Phys. Rev. B: Condens. Matter 1984, 30, 4267. <https://doi.org/10.1103/PhysRevB.30.4267>
3p. Paldus J., Piecuch P.: Int. J. Quantum Chem. 1992, 42, 135. <https://doi.org/10.1002/qua.560420110>
3q. Li X., Paldus J.: J. Chem. Phys. 2003, 119, 5334. <https://doi.org/10.1063/1.1599302>
3r. Stuber J. L., Paldus J. in: Fundamental World of Quantum Chemistry (E. J. Brändas and E. S. Kryachko, Eds), Vol. I. Kluwer, Dordrecht 2003.
4a. Ge M.-L., Su G.: J. Phys. A: Math. Gen. 1991, 24, L721. <https://doi.org/10.1088/0305-4470/24/13/004>
4b. Martín-Delgado M. A.: J. Phys. A: Math. Gen. 1991, 24, L1285. <https://doi.org/10.1088/0305-4470/24/21/006>
4c. Lee C. R., Yu J.-P.: Phys. Lett. A 1992, 164, 164. <https://doi.org/10.1016/0375-9601(92)90696-J>
4d. Su G., Ge M.-L.: Phys. Lett. A 1993, 173, 17. <https://doi.org/10.1016/0375-9601(93)90079-F>
4e. Tuszyński J. A., Rubin J. L., Meyer J., Kibler M.: Phys. Lett. A 1993, 175, 173. <https://doi.org/10.1016/0375-9601(93)90822-H>
4f. Man’ko V. I., Marmo G., Solimeno S., Zaccaria F.: Phys. Lett. A 1993, 176, 173. <https://doi.org/10.1016/0375-9601(93)91029-5>
4g. Hsu R.-R., Lee C.-R.: Phys. Lett. A 1993, 180, 314. <https://doi.org/10.1016/0375-9601(93)91183-6>
4h. Granovskii Ya. I., Zhedanov A. S.: Mod. Phys. Lett. A 1993, 8, 1029. <https://doi.org/10.1142/S0217732393002518>
4i. Chaichian M., Felipe R. G., Montonen C.: J. Phys. A: Math. Gen. 1993, 26, 4017. <https://doi.org/10.1088/0305-4470/26/16/018>
4j. Gupta R. K., Bach C. T., Rosu H.: J. Phys. A: Math. Gen. 1994, 27, 1427. <https://doi.org/10.1088/0305-4470/27/5/010>
4k. Monteiro M. A. R., Roditi I., Rodrigues L. M. C. S.: Phys. Lett. A 1994, 188, 11. <https://doi.org/10.1016/0375-9601(94)90109-0>
4l. Gong R.-S.: Phys. Lett. A 1995, 199, 81. <https://doi.org/10.1016/0375-9601(95)00080-M>
4m. Daoud M., Kibler M.: Phys. Lett. A 1995, 206, 13. <https://doi.org/10.1016/0375-9601(95)00580-V>
5a. Witten E.: Nucl. Phys. B 1990, 330, 285. <https://doi.org/10.1016/0550-3213(90)90115-T>
5b. Iwao S.: Prog. Theor. Phys. 1990, 83, 363. <https://doi.org/10.1143/PTP.83.363>
5c. Bonatsos D., Raychev P. P., Roussev R. P., Smirnov Yu. F.: Chem. Phys. Lett. 1990, 175, 300. <https://doi.org/10.1016/0009-2614(90)80114-S>
5d. Chang Z., Yan H.: Phys. Lett. A 1991, 154, 254. <https://doi.org/10.1016/0375-9601(91)90816-Q>
5e. Chang Z., Guo H.-Y., Yan H.: Phys. Lett. A 1991, 156, 192. <https://doi.org/10.1016/0375-9601(91)90936-3>
5f. Chang Z., Yan H.: Phys. Lett. A 1991, 158, 242. <https://doi.org/10.1016/0375-9601(91)91007-Z>
5g. Bonatsos D., Drenska S. B., Raychev P. P., Roussev R. P., Smirnov Yu. F.: J. Phys. G: Nucl. Part. Phys. 1991, 17, L67. <https://doi.org/10.1088/0954-3899/17/5/003>
5h. Bonatsos D., Raychev P. P., Faessler A.: Chem. Phys. Lett. 1991, 178, 221. <https://doi.org/10.1016/0009-2614(91)87060-O>
5i. Bonatsos D., Argyres E. N., Raychev P. P.: J. Phys. A: Math. Gen. 1991, 24, L403. <https://doi.org/10.1088/0305-4470/24/8/003>
5j. Jenkovszky L., Kibler M., Mishchenko A.: Mod. Phys. Lett. A 1995, 10, 51. <https://doi.org/10.1142/S0217732395000065>
5k. Barbier R., Kibler M. in: Finite Dimensional Integrable Systems (A. N. Sissakian and G. S. Pogosyan, Eds). JINR, Dubna 1995.
5l. Barbier R., Kibler M. in: Modern Group Theoretical Methods in Physics (J. Bertrand, M. Flato, J.-P. Gazeau, D. Sternheimer and M. Irac-Astaud, Eds). Kluwer, Dordrecht 1995.
5m. Barbier R., Kibler M.: Rep. Math. Phys. 1996, 38, 221. <https://doi.org/10.1016/0034-4877(96)88953-1>
6a. Wigner E. P.: Z. Phys. 1927, 43, 624. <https://doi.org/10.1007/BF01397327>
6b. Wigner E. P.: Am. J. Math. 1941, 63, 57. <https://doi.org/10.2307/2371276>
6c. Wigner E. P.: Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra. Academic Press, New York 1959.
6d. Wigner E. P. in: Quantum Theory of Angular Momemtum (L. C. Biedenharn and H. van Dam, Eds). Academic Press, New York 1965.
6e. Wigner E. P. in: Spectroscopic, Group Theoretical Methods in Physics (F. Bloch, S. G. Cohen, A. de-Shalit, S. Sambursky and I. Talmi, Eds). North-Holland, Amsterdam 1968.
6f. Wigner E. P.: Proc. R. Soc. London, Ser. A 1971, 322, 181. <https://doi.org/10.1098/rspa.1971.0062>
6g. Goldrich F. G., Wigner E. P.: Can. J. Math. 1972, 24, 432. <https://doi.org/10.4153/CJM-1972-036-3>
6h. Wigner E. P.: SIAM J. Appl. Math. 1973, 25, 169. <https://doi.org/10.1137/0125022>
7a. Racah G.: Phys. Rev. 1942, 61, 186. <https://doi.org/10.1103/PhysRev.61.186>
7b. Racah G.: Phys. Rev. 1942, 62, 438. <https://doi.org/10.1103/PhysRev.62.438>
7c. Racah G.: Phys. Rev. 1943, 63, 367. <https://doi.org/10.1103/PhysRev.63.367>
7d. Racah G.: Phys. Rev. 1949, 76, 1352. <https://doi.org/10.1103/PhysRev.76.1352>
7e. Racah G.: Phys. Rev. 1950, 78, 622. <https://doi.org/10.1103/PhysRev.78.622>
7f. Racah G.: Bull. Res. Council Isr., Sect. F 1959, 8, 1.
7g. Racah G.: Ergebnisse der exakten Naturwissenschaften, Vol. 37, p. 27. Springer-Verlag, Berlin 1965.
7h. Fano U., Racah G.: Irreducible Tensorial Sets. Academic Press, New York 1959.
7i. Racah G., Stein J.: Phys. Rev. 1967, 156, 58. <https://doi.org/10.1103/PhysRev.156.58>
8a. Grenet G., Kibler M.: Phys. Lett. A 1978, 68, 147. <https://doi.org/10.1016/0375-9601(78)90786-7>
8b. Grenet G., Kibler M.: Phys. Lett. A 1979, 71, 323. <https://doi.org/10.1016/0375-9601(79)90066-5>
8c. Kibler M., Grenet G.: J. Math. Phys. 1980, 21, 422. <https://doi.org/10.1063/1.524439>
9a. Kibler M.: J. Mol. Spectrosc. 1968, 26, 111. <https://doi.org/10.1016/0022-2852(68)90148-3>
9b. Kibler M.: Int. J. Quantum Chem. 1969, 3, 795. <https://doi.org/10.1002/qua.560030606>
9c. Kibler M.: C. R. Acad. Sci., Ser. B 1969, 268, 1221.
9d. Kibler M. R.: J. Math. Phys. 1976, 17, 855. <https://doi.org/10.1063/1.522996>
9e. Kibler M. R.: J. Mol. Spectrosc. 1976, 62, 247. <https://doi.org/10.1016/0022-2852(76)90353-2>
9f. Kibler M. R.: J. Phys. A: Math. Gen. 1977, 10, 2041. <https://doi.org/10.1088/0305-4470/10/12/013>
9g. Kibler M. R., Guichon P. A. M.: Int. J. Quantum Chem. 1976, 10, 87. <https://doi.org/10.1002/qua.560100108>
9h. Kibler M. R., Grenet G.: Int. J. Quantum Chem. 1977, 11, 359. <https://doi.org/10.1002/qua.560110216>
9i. Kibler M. R.: Int. J. Quantum Chem. 1983, 23, 115. <https://doi.org/10.1002/qua.560230113>
10a. Moret-Bailly J.: J. Mol. Spectrosc. 1965, 15, 344. <https://doi.org/10.1016/0022-2852(65)90150-5>
10b. Champion J. P., Pierre G., Michelot F., Moret-Bailly J.: Can. J. Phys. 1977, 55, 512. <https://doi.org/10.1139/p77-070>
10c. Patera J., Winternitz P.: J. Math. Phys. 1973, 14, 1130. <https://doi.org/10.1063/1.1666449>
10d. Patera J., Winternitz P.: J. Chem. Phys. 1976, 65, 2725. <https://doi.org/10.1063/1.433416>
10e. Michel L. in: Group Theoretical Methods in Physics (R. T. Sharp and B. Kolman, Eds). Academic Press, New York 1977.
11a. Arik M., Coon D. D.: J. Math. Phys. 1976, 17, 524. <https://doi.org/10.1063/1.522937>
11b. Biedenharn L. C.: J. Phys. A: Math. Gen. 1989, 22, L873. <https://doi.org/10.1088/0305-4470/22/18/004>
11c. Sun C.-P., Fu H.-C.: J. Phys. A: Math. Gen. 1989, 22, L983. <https://doi.org/10.1088/0305-4470/22/21/001>
11d. Macfarlane A. J.: J. Phys. A: Math. Gen. 1989, 22, 4581. <https://doi.org/10.1088/0305-4470/22/21/020>
11e. Fairlie D. B., Fletcher P., Zachos C. K.: J. Math. Phys. 1990, 31, 1088. <https://doi.org/10.1063/1.528788>
11f. Greenberg O. W.: Phys. Rev. D: Part. Fields 1991, 43, 4111. <https://doi.org/10.1103/PhysRevD.43.4111>
11g. Rideau G.: Lett. Math. Phys. 1992, 24, 147. <https://doi.org/10.1007/BF00402678>
11h. Kibler M. R. in: Symmetry, Structural Properties of Condensed Matter (W. Florek, D. Lipiński and T. Lulek, Eds). World Scientific, Singapore 1993.
11i. Daoud M., Hassouni Y., Kibler M. in: Symmetries in Science X (B. Gruber and M. Ramek, Eds). Plenum Press, New York 1998.
11j. Daoud M., Kibler M.: Phys. Lett. A 2004, 321, 147. <https://doi.org/10.1016/j.physleta.2003.12.027>
11k. Kibler M., Daoud M. in: Fundamental World of Quantum Chemistry (E. J. Brändas and E. S. Kryachko, Eds), Vol. III. Kluwer, Dordrecht 2003.
12. Schwinger J. in: Quantum Theory of Angular Momentum (L. C. Biedenharn and H. van Dam, Eds). Academic Press, New York 1965.
13. Lévy-Leblond J.-M.: Rev. Mex. Fis. 1973, 22, 15.
14. Edmonds A. R.: Angular Momentum in Quantum Mechanics. Princeton University Press, Princeton 1960.
15a. Vourdas A.: Phys. Rev. A: At., Mol., Opt. Phys. 1990, 41, 1653. <https://doi.org/10.1103/PhysRevA.41.1653>
15b. Vourdas A.: Phys. Rev. A: At., Mol., Opt. Phys. 1991, 43, 1564. <https://doi.org/10.1103/PhysRevA.43.1564>
15c. Vourdas A., Bendjaballah C.: Phys. Rev. A: At., Mol., Opt. Phys. 1993, 47, 3523. <https://doi.org/10.1103/PhysRevA.47.3523>
15d. Vourdas A.: J. Phys. A: Math. Gen. 1996, 29, 4275. <https://doi.org/10.1088/0305-4470/29/14/043>
15e. Planat M., Rosu H. C.: Phys. Lett. A 2003, 315, 1. <https://doi.org/10.1016/S0375-9601(03)00942-3>
15f. Planat M., Rosu H.: J. Opt. B: Quantum Semiclassical Opt. 2004, 6, S583. <https://doi.org/10.1088/1464-4266/6/6/018>
15g. Saniga M., Planat M., Rosu H.: J. Opt. B: Quantum Semiclassical Opt. 2004, 6, L19. <https://doi.org/10.1088/1464-4266/6/9/L01>