Quantum groups and deformed special relativity

Fortschritte der Physik

Volumn 44, Issue 1, 1996, Pages 1-40

  De Azcarraga J A ^a   Kulish, P P ^a   Rodenas, F ^a,b  

^a INSTITUTO DE FÍSICA CORPUSCULAR IFIC   (Spain)

^b UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030524924     PISSN: 00158208     EISSN: None     Source Type: Journal    
DOI: 10.1002/prop.2190440102     Document Type: Article

References (120)

1. V. G. DRINFEL'D, in Proc. of the 1986 Internat. Congr. Mathematicians, MSRI Berkeley, vol I, 798 (1987) (A. Gleason, ed.).
2. M. JIMBO, Lett. Math. Phys. 10, 63 (1985); ibid 11, 247 (1986).
3. M. JIMBO, Lett. Math. Phys. 10, 63 (1985); ibid 11, 247 (1986).
4. L. D. FADDEEV, N. YU. RESHETIKHIN and L. A. TAKHTAJAN, Alg. i Anal. 1, 178 (1989) Leningrad Math. J. 1, 193 (1990)).
5. L. D. FADDEEV, N. YU. RESHETIKHIN and L. A. TAKHTAJAN, Alg. i Anal. 1, 178 (1989) Leningrad Math. J. 1, 193 (1990)).
6. S. L. WORONOWICZ, Publ. RIMS Kyoto Univ. 23, 117 (1987).
7. P. PODLEŚ and S. WORONOWICZ, Commun. Math. Phys. 130, 381 (1990).
8. U. CAROW-WATAMURA, M. SCHLIEKER, M. SCHOLL and S. WATAMURA, Z. Phys. C48, 159 (1990).
9. U. CAROW-WATAMURA, M. SCHLIEKER, M. SCHOLL and S. WATAMURA, Internat. J. Mod. Phys. A6, 3081 (1991).
10. W. SCHMIDKE, J. WESS and B. ZUMINO, Z. Phys. C52, 471 (1991).
11. O. OGIEVETSKY, W. B. SCHMIDKE, J. WESS and B. ZUMINO, Commun. Math. Phys. 150, 495 (1992).
12. X-C. SONG, Z. Phys. C55, 417 (1992).
13. S. P. VOKOS, B. ZUMINO and J. WESS, Z. Phys. C48, 65 (1990).
14. E. CORRIGAN, D. B. FAIRLIE, P. FLETCHER and R. SASAKI, J. Math. Phys. 31, 776 (1990).
15. L. D. FADDEEV Sov. Sci. Rev., Sec. C (Math. Phys.) 1, 107 (1980); P. P. KULISH and E. K. SKLYANIN, Lect. Notes in Phys. 151, 61 (1981); A. G. IZERGIN and V. E. KOREPIN, Fisika EChAYa 13, 501 (1982); F. A. SMIRNOV, Form factors in completely integrable models, World Sci. (1992); E. K. SKLYANIN, in Quantum groups and quantum integrable systems, (M.-L. Ge ed.), World Sci. (1992), p. 63.
16. L. D. FADDEEV Sov. Sci. Rev., Sec. C (Math. Phys.) 1, 107 (1980); P. P. KULISH and E. K. SKLYANIN, Lect. Notes in Phys. 151, 61 (1981); A. G. IZERGIN and V. E. KOREPIN, Fisika EChAYa 13, 501 (1982); F. A. SMIRNOV, Form factors in completely integrable models, World Sci. (1992); E. K. SKLYANIN, in Quantum groups and quantum integrable systems, (M.-L. Ge ed.), World Sci. (1992), p. 63.
17. L. D. FADDEEV Sov. Sci. Rev., Sec. C (Math. Phys.) 1, 107 (1980); P. P. KULISH and E. K. SKLYANIN, Lect. Notes in Phys. 151, 61 (1981); A. G. IZERGIN and V. E. KOREPIN, Fisika EChAYa 13, 501 (1982); F. A. SMIRNOV, Form factors in completely integrable models, World Sci. (1992); E. K. SKLYANIN, in Quantum groups and quantum integrable systems, (M.-L. Ge ed.), World Sci. (1992), p. 63.
18. L. D. FADDEEV Sov. Sci. Rev., Sec. C (Math. Phys.) 1, 107 (1980); P. P. KULISH and E. K. SKLYANIN, Lect. Notes in Phys. 151, 61 (1981); A. G. IZERGIN and V. E. KOREPIN, Fisika EChAYa 13, 501 (1982); F. A. SMIRNOV, Form factors in completely integrable models, World Sci. (1992); E. K. SKLYANIN, in Quantum groups and quantum integrable systems, (M.-L. Ge ed.), World Sci. (1992), p. 63.
19. L. D. FADDEEV Sov. Sci. Rev., Sec. C (Math. Phys.) 1, 107 (1980); P. P. KULISH and E. K. SKLYANIN, Lect. Notes in Phys. 151, 61 (1981); A. G. IZERGIN and V. E. KOREPIN, Fisika EChAYa 13, 501 (1982); F. A. SMIRNOV, Form factors in completely integrable models, World Sci. (1992); E. K. SKLYANIN, in Quantum groups and quantum integrable systems, (M.-L. Ge ed.), World Sci. (1992), p. 63.
20. L. A. TAKHTAJAN, Lectures in quantum groups, in Nankai Lectures in Math. Phys. (M.-L. Ge and B.-H. Zhao eds.), World Sci. (1990), p. 69.
21. V. CHARI and A. PRESSLEY, Nucl. Phys. (Proc. Suppl.) 18A, 207 (1990); A guide to quantum groups, CUP (1994).
22. V. CHARI and A. PRESSLEY, Nucl. Phys. (Proc. Suppl.) 18A, 207 (1990); A guide to quantum groups, CUP (1994).
23. S. MAJID, Internat. J. Mod. Phys. A5, 1 (1990).
24. H. D. DOEBNER, J. D. HENNING and W. LÜCKE, Mathematical guide to quantum groups, in Proc. of the Clausthal Int. Workshop on Math. Phys., H.-D. Doebner and J.-D. Henning Eds., Springer-Verlag (1990), p. 29.
25. YU. I. MANIN, Commun. Math. Phys. 123, 163 (1989); Topics in non-commutative geometry, Princeton Univ. Press (1991).
26. YU. I. MANIN, Commun. Math. Phys. 123, 163 (1989); Topics in non-commutative geometry, Princeton Univ. Press (1991).
27. J. WESS and B. ZUMINO, Nucl. Phys. (Proc. Suppl.) 18B, 302 (1990); See also the contributions of J. WESS and B. ZUMINO to the Proc. of the XIX Int. Coll. on Group Theor. Methods in Phys., Salamanca, 1992 (M. A. DEL OLMO, M. SANTANDER and J. MATEOS GUILARTE eds.), Anales de Física: Monografías 1, vol. I, pp.33 and 41 respectively (1993).
28. J. WESS and B. ZUMINO, Nucl. Phys. (Proc. Suppl.) 18B, 302 (1990); See also the contributions of J. WESS and B. ZUMINO to the Proc. of the XIX Int. Coll. on Group Theor. Methods in Phys., Salamanca, 1992 (M. A. DEL OLMO, M. SANTANDER and J. MATEOS GUILARTE eds.), Anales de Física: Monografías 1, vol. I, pp.33 and 41 respectively (1993).
29. P. P. KULISH and E. K. SKLYANIN, J. Phys. A25, 5963 (1992).
30. P. P. KULISH and R. SASAKI, Progr. Theor. Phys. 89, 741 (1993).
31. P. P. KULISH, Theor. and Math. Phys. 94, 137 (1993) Teor. i Mat. Fiz. 94, 193 (1993)).
32. P. P. KULISH, Theor. and Math. Phys. 94, 137 (1993) Teor. i Mat. Fiz. 94, 193 (1993)).
33. I. CHEREDNIK, Theor. and Math. Phys. 61, 55 (1984).
34. E. SKLYANIN, J. Phys. A21, 2375 (1988).
35. L. MEZINCESCU and R. NEPOMECHIE, J. Phys. A24, L17 (1991).
36. MAJID S., in Quantum Groups, Lect. Notes Math. 1510, 79 (1992) (P. P. Kulish, ed.); J. Math. Phys. 32, 3246 (1991).
37. MAJID S., in Quantum Groups, Lect. Notes Math. 1510, 79 (1992) (P. P. Kulish, ed.); J. Math. Phys. 32, 3246 (1991).
38. S. MAJID, J. Math. Phys. 34, 1176 (1993); J. Geom. Phys. 13, 169 (1994).
39. S. MAJID, J. Math. Phys. 34, 1176 (1993); J. Geom. Phys. 13, 169 (1994).
40. L. FREIDEL and J. M. MAILLET, Phys. Lett. B262, 278 (1991).
41. G. MACK and V. SCHOMERUS, Nucl. Phys. B370, 185 (1992).
42. N. YU. RESHETIKHIN and F. SMIRNOV, Commun. Math. Phys. 131, 157 (1990).
43. M. PILLIN, W. B. SCHMIDKE and J. WESS, Nucl. Phys. B403, 223 (1993); Proceed. XXVI Internat. Symp. Theory of Elem. Particles, DESY 93-013, 72, 99 (1993).
44. M. PILLIN, W. B. SCHMIDKE and J. WESS, Nucl. Phys. B403, 223 (1993); Proceed. XXVI Internat. Symp. Theory of Elem. Particles, DESY 93-013, 72, 99 (1993).
45. M. PILLIN, J. Math. Phys. 35, 2804 (1994).
46. A. SCHIRRMACHER, Lett. Math. Phys. 29, 329 (1993).
47. q(3)-symmetry, München LMU-TPW 93-27.
48. U. WATAMURA, M. SCHLIEKER and S. WATAMURA, Z. Phys. C49, 439 (1991).
49. O. OGIEVETSKY and B. ZUMINO, Lett. Math. Phys. 25, 121 (1992).
50. J. A. DE AZCÁRRAGA, P. P. KULISH and F. RODENAS, Phys. Lett. B351, 123 (1995).
51. C. GÓMEZ and G. SIERRA, Phys. Lett. B255, 51 (1991).
52. V. K. DOBREV, q-deformations of non-compact Lie (Super-) Algebras: the examples of q-deformed Lorentz, Poincaré and (Super-) conformal algebra, in Proc. of the II Wigner Symposium, Goslar (1991), Springer Verlag; J. Phys. A26, 1317 (1993).
53. V. K. DOBREV, q-deformations of non-compact Lie (Super-) Algebras: the examples of q-deformed Lorentz, Poincaré and (Super-) conformal algebra, in Proc. of the II Wigner Symposium, Goslar (1991), Springer Verlag; J. Phys. A26, 1317 (1993).
54. M. CHAICHIAN, J. A. DE AZCÁRRAGA and F. RODENAS, q-Fock space representations of the q-Lorentz algebra and irreducible tensors, in Symmetries in Science VI, B. Gruber ed., Plenum Press (1994), p. 157.
55. W. PUSZ, Commun. Math. Phys. 152, 591 (1993).
56. L. CASTELLANI, Phys. Lett. B298, 335 (1993).
57. S. MAJID, J. Math. Phys. 34, 2045 (1993).
58. A. BALLESTEROS, F. J. HERRANZ, M. A. DEL OLMO and M. SANTANDER, J. Math. Phys. 35, 4928 (1994); J. Phys. A27, 1283 (1994).
59. A. BALLESTEROS, F. J. HERRANZ, M. A. DEL OLMO and M. SANTANDER, J. Math. Phys. 35, 4928 (1994); J. Phys. A27, 1283 (1994).
60. P. PODLEŚ and S. L. WORONOWICZ, On the classification of quantum Poincaré groups, hep-th 9412059.
61. q,r(N), DFTT-44/94, hep-th 9411039.
62. E. CELEGHINI, R. GIACHETTI, E. SORACE and M. TARLINI, J. Math. Phys. 31, 2548 (1990); ibid. 32, 1155, 1159 (1991).
63. E. CELEGHINI, R. GIACHETTI, E. SORACE and M. TARLINI, J. Math. Phys. 31, 2548 (1990); ibid. 32, 1155, 1159 (1991).
64. J. LUKIERSKI, A. NOWICKI, H. RUEGG and V. N. TOLSTOI, Phys. Lett. B264, 331 (1991); J. LUKIERSKI, A. NOWICKI and H. RUEGG, Phys. Lett. B293, 344 (1992); J. Geom. Phys. 11, 425 (1993).
65. J. LUKIERSKI, A. NOWICKI, H. RUEGG and V. N. TOLSTOI, Phys. Lett. B264, 331 (1991); J. LUKIERSKI, A. NOWICKI and H. RUEGG, Phys. Lett. B293, 344 (1992); J. Geom. Phys. 11, 425 (1993).
66. J. LUKIERSKI, A. NOWICKI, H. RUEGG and V. N. TOLSTOI, Phys. Lett. B264, 331 (1991); J. LUKIERSKI, A. NOWICKI and H. RUEGG, Phys. Lett. B293, 344 (1992); J. Geom. Phys. 11, 425 (1993).
67. H. RUEGG, q-deformation of semisimple and simple algebras, in Integrable systems, quantum groups and quantum field theories (Salamanca 1992), L. A. Ibort and M. A. Rodriguez eds. NATO-ASI 409, Kluwer (1993) p. 45.
68. J. LUKIERSKI, H. RUEGG and W. J. ZAKRZEWSKI, Classical and quantum mechanics of free κ-relativistic systems, hep-th 9312153, to appear in Ann. Phys.
69. S. MAJID and H. RUEGG, Phys. Lett. B334, 348 (1994).
70. A. SITARZ, Phys. Lett. B349, 42 (1995).
71. J. A. DE AZCÁRRAGA and J. C. PÉREZ BUENO, Relativistic and non-relativistic κ-spacetimes, q-alg 9505004, to appear in J. Math. Phys.
72. S. L. WORONOWICZ and S. ZAKRZEWSKI, Composiktio Math. 94, 211 (1994).
73. U. MEYER, The q-Lorent: group and braided coaddition on q-Minkowski space, DAMTP 93-45 (revised, Jan. 1994), to appear in Commun. Math. Phys.
74. J. A. DE AZCÁRRAGA, P. P. KULISH and F. RODENAS, Lett. Math. Phys. 32, 173 (1994).
75. S. MAJID and U. MEYER, Z. Phys. C63, 357 (1994).
76. B. ZUMINO, Introduction to the differential geometry of quantum groups, in Mathematical Physics X, K. Schmüdgen ed., Springer-Verlag (1992), p. 20.
77. X-C. SONG, J. Phys. A25, 2929 (1992).
78. B. DRABANT, M. SCHLIEKER, W. WEICH and B. ZUMINO, Commun. Math. Phys. 147, 625 (1992).
79. J. A. DE AZCÁRRAGA, P. P. KULISH and F. RODENAS, Czech. J. Phys. 44, 981 (1994).
80. S. MAJID, J. Math. Phys. 35, 5025 (1994).
81. S. MAJID, Some remarks of the q-Poincaré algebra in R-matrix form, DAMTP/95-08, q-alg/9502014.
82. M. CHAICHIAN and A. DEMICHEV, Phys. Lett. B304, 220 (1993); J. Math. Phys. 36, 398 (1995).
83. M. CHAICHIAN and A. DEMICHEV, Phys. Lett. B304, 220 (1993); J. Math. Phys. 36, 398 (1995).
84. J. LUKIERSKI, H. RUEGG, V. N. TOLSTOI and A. NOWICKI, J. Phys. A27, 2389 (1994).
85. V. DRINFEL'D, Alg. i Anal. 1, 30 Leningrad Math. J. 1, 1419 (1990)).
86. V. DRINFEL'D, Alg. i Anal. 1, 30 Leningrad Math. J. 1, 1419 (1990)).
87. N. RESHETIKHIN, Lett. Math. Phys. 20, 331 (1990).
88. S. L. WORONOWICZ, Commun. Math. Phys. 122, 125 (1989).
89. P. SCHUPP, P. WATTS and B. ZUMINO, Lett. Math. Phys. 25, 139 (1992).
90. YU. I. MANIN, Theor. and Math. Phys. 92, 997 (1993) Theor. and Math. Fiz. 92, 425 (1992)).
91. YU. I. MANIN, Theor. and Math. Phys. 92, 997 (1993) (Theor. and Math. Fiz. 92, 425 (1992)).
92. A. SUDBERY, Phys. Lett. B284, 61 (1992).
93. L. D. FADDEEV and P. N. PYATOV, The differential calculus on quantum linear groups, preprint (1993), hep-th 9402070.
94. P. P. KULISH, Zap. Nauch. Semin. POMI 205, 66 (1993).
95. q and the theory of q-tensor operators, in Proc. of the Clausthal Int. Workshop on Math. Physics, H.-D. Doebner and J.-D. Henning eds., Springer-Verlag (1990), p. 67.
96. q and the theory of q-tensor operators, in Proc. of the Clausthal Int. Workshop on Math. Physics, H.-D. Doebner and J.-D. Henning eds., Springer-Verlag (1990), p. 67.
97. V. RITTENBERG and M. SCHEUNERT, J. Math. Phys. 33, 436 (1992).
98. FENG PAN, J. Phys. A24, L803 (1991); L. K. HADJIIVANOV, R. R. PAUNOV and I. T. TODOROV, J. Math. Phys. 33, 1379 (1992).
99. FENG PAN, J. Phys. A24, L803 (1991); L. K. HADJIIVANOV, R. R. PAUNOV and I. T. TODOROV, J. Math. Phys. 33, 1379 (1992).
100. A. SCHIRRMACHER, Quantum groups, quantum space-time and Dirac equation, MPI-PTh/92-92 (1992). Talk given at the workshop on Low dimensional topology and quantum field theory, Newton Inst. (Cambridge), Sep. 1992.
101. U. MEYER, Wave equations on q-Minkowski spaces, DAMTP 94-10 (1994), hep-th 9404054.
102. U. H. NIEDERER and L. O'RAIFEARTAIGH, Fortschr. Phys. 22, 111, 131 (1974); J. A. DE AZCÁRRAGA and L. J. BOYA, J. Math. Phys. 9, 1689 (1968).
103. U. H. NIEDERER and L. O'RAIFEARTAIGH, Fortschr. Phys. 22, 111, 131 (1974); J. A. DE AZCÁRRAGA and L. J. BOYA, J. Math. Phys. 9, 1689 (1968).
104. J. WESS, q-deformed quantization, LMU München preprint (1994).
105. P. P. KULISH, Teor. Matem. Fiz. 86, 157 (1991) Theor. Math. Phys. 86, 108 (1991)).
106. P. P. KULISH, Teor. Matem. Fiz. 86, 157 (1991) (Theor. Math. Phys. 86, 108 (1991)).
107. G. RIDEAU, Lett. Math. Phys. 24, 147 (1992).
108. O. OGIEVETSKII, W. B. SCHMIDKE, J. WESS and B. ZUMINO, Lett. Math. Phys. 23, 233 (1991).
109. P. P. KULISH, Alg. i Anal. 6, 195 (1994).
110. P. PODLEŚ, Lett. Math. Phys. 14, 193 (1987).
111. M. NOUMI and K. MIMACHI, Duke Math. Jour. 63, 65 (1991).
112. A. ALEKSEEV, L. D. FADDEEV and M. A. SEMENOV-TIAN-SHANSKY, in Quantum Groups, Lect. Notes Math. 1510, 148 (1992) (P. P. Kulish, ed.).
113. A. P. ISAEV and A. A. VLADIMIROV, Lett. Math. Phys. 33, 297 (1995).
114. E. CREMMER and J.-L. GERVAIS, Commun. Math. Phys. 144, 279 (1991).
115. V. G. DRINFEL'D, Sov. Math. Dokl. 27, 68 (1983).
116. M. A. SEMENOV-TIAN-SHANSKY, Publ. RIMS 21, 1237 (1985).
117. M. FLATO and D. STERNHEIMER, Lett. Math. Phys. 22, 155 (1991); Alg. i Anal. 6, (1994).
118. M. FLATO and D. STERNHEIMER, Lett. Math. Phys. 22, 155 (1991); Alg. i Anal. 6, (1994).
119. C. CHRISSOMALAKOS and B. ZUMINO, Translations, integrals and Fourier transform in the quantum plane, UCB-PTH 93/30.
120. A. KEMPF and S. MAJID, J. Math. Phys. 35, 6802 (1994).