Variations on a theme of Heisenberg, Pauli and Weyl

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 37, 2008, Pages

  Kibler, Maurice R ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749122085     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/37/375302     Document Type: Article

References (95)

1. Heisenberg W 1925 Z. Phys. 33 879
2. Pauli W Jr 1927 Z. Phys. 43 601
3. Weyl H 1927 Z. Phys. 46 1
4. Weyl H 1931 The Theory of Groups and Quantum Mechanics (New York: Dover)
5. Wolf K B and García A 1972 Rev. Mex. Fís. 21 191
6. Wolf K B 1975 The Heisenberg-Weyl ring in quantum mechanics Group Theory and its Applications vol 3 ed E M Loebl (New York: Academic)
7. García-Bullé M, Lassner W and Wolf K B 1986 J. Math. Phys. 27 29
8. Atakishiyev N M, Pogosyan G S and Wolf K B 2003 Int. J. Mod. Phys. A 18 317
9. Daoud M and Kibler M R 2006 J. Math. Phys. 47 122108
10. ovíek P and Tolar J 1984 Rep. Math. Phys. 20 157
11. Balian R and Itzykson C 1986 C. R. Acad. Sci., Paris 303 773
12. Patera J and Zassenhaus H 1988 J. Math. Phys. 29 665
13. Terras A 1996 Exp. Math. 5 15
14. Terras A 1999 Fourier Analysis on Finite Groups and Applications (Cambridge: Cambridge University Press)
15. Howe R 2005 Indag. Math., N.S. 16 553
16. Vourdas A 2005 J. Phys. A: Math. Gen. 38 8453
17. Vourdas A 2006 J. Math. Phys. 47 092104
18. Vourdas A 2007 J. Phys. A: Math. Theor. 40 R285
19. Vourdas A 2008 Private communication
20. Fivel D I 1995 Phys. Rev. Lett. 74 835
21. Schwinger J 1960 Proc. Natl Acad. Sci. USA 46 570
22. McIntosh H V 1962 J. Mol. Spectrosc. 8 169
23. Gell-Mann M 1962 Phys. Rev. 125 1067
24. Ne'eman Y 1961 Nucl. Phys. 26 222
25. Okubo S 1962 Prog. Theor. Phys., Kyoto 27 949
26. Glashow S L, Iliopoulos J and Maiani L 1970 Phys. Rev. D 2 1285
27. Georgi H and Glashow S L 1974 Phys. Rev. Lett. 32 438
28. de Azcrraga J A and Macfarlane A J 2001 Int. J. Mod. Phys. A 16 1377
29. Knill E 1996 Preprint quant-ph/9608048
30. Gottesman D 1999 Chaos Solitons Fractals 10 1749
31. Gottesman D, Kitaev A and Preskill J 2001 Phys. Rev. A 64 012310
32. Gibbons K S, Hoffman M J and Wootters W K 2004 Phys. Rev. A 70 062101
33. Pittenger A O and Rubin M H 2000 Phys. Rev. A 62 032313
34. Pittenger A O and Rubin M H 2004 Linear Algebr. Appl. 390 255
35. Pittenger A O and Rubin M H 2005 J. Phys. A: Math. Gen. 38 6005
36. Bandyopadhyay S, Boykin P O, Roychowdhury V and Vatan F 2002 Algorithmica 34 512
37. Lawrence J, Brukner and Zeilinger A 2002 Phys. Rev. A 65 032320
38. Vlasov A Yu 2003 Preprint quant-ph/0302064
39. Klimov A B, Snchez-Soto L L and de Guise H 2005 J. Opt. B: Quantum Semiclass. Opt. 7 283
40. Klimov A B, Snchez-Soto L L and de Guise H 2005 J. Phys. A: Math. Gen. 38 2747
41. King C, Matsumoto K, Nathanson M and Ruskai M B 2005 Preprint quant-ph/0509126
42. Nathanson M and Ruskai M B 2007 J. Phys. A: Math. Theor. 40 8171
43. Ballester M A and Wehner S 2007 Phys. Rev. A 75 022319
44. Planat M, Saniga M and Kibler M R 2006 SIGMA 2 066
45. Saniga M, Planat M, Pracna P and Havlicek H 2007 SIGMA 3 075
46. Planat M, Baboin A-C and Saniga M 2008 Int. J. Theor. Phys. 47 1127
47. Planat M and Saniga M 2008 Quantum Inf. Comput. 8 0127
48. Saniga M, Planat M and Pracna P 2008 Theor. Math. Phys. 155 463
49. Aschbacher M, Childs A M and Wocjan P 2007 J. Algebr. Comb. 25 111
50. Fujii K 2007 Int. G. Geom. Methods Mod. Phys. 4 1205
51. Lawrence J 2004 Phys. Rev. A 70 012302
52. Grassl M 2005 On SIC-POVMs and MUBs in dimension 6 Proc. ERATO Conf. Quantum Information Science (EQIS 2004) ed J Gruska (Tokyo)
53. Grassl M 2005 Elec. Notes Discrete Math. 20 151
54. Durt T 2005 J. Phys. A: Math. Gen. 38 5267
55. Appleby D M 2005 J. Math. Phys. 46 052107
56. Flammia S T 2006 J. Phys. A: Math. Gen. 39 13483
57. Cormick C, Galvo E F, Gottesman D, Paz J P and Pittenger A O 2006 Phys. Rev. A 73 012301
58. ulc P and Tolar J 2007 J. Phys. A: Math. Theor. 40 15099
59. Albouy O and Kibler M R 2007 SIGMA 3 076
60. Havlicek H and Saniga M 2007 J. Phys. A: Math. Theor. 40 F943
61. Planat M and Baboin A-C 2007 J. Phys. A: Math. Theor. 40 F1005
62. Havlicek H and Saniga M 2008 J. Phys. A: Math. Theor. 41 015302
63. Planat M and Jorrand Ph 2008 J. Phys. A: Math. Theor. 41 182001
64. Wigner E P 1941 Am. J. Math. 63 57
65. Wigner E P 1965 On the matrices which reduce the Kronecker products of representations of S.R. groups Quantum Theory of Angular Momemtum ed L C Biedenharn and H van Dam (New York: Academic)
66. Lambert D and Kibler M 1988 J. Phys. A: Math. Gen. 21 307
67. Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
68. Gamba A 1969 J. Math. Phys. 10 872
69. Edmonds A R 1960 Angular Momentum in Quantum Mechanics (Princeton, NJ: Princeton University Press)
70. 2 in a non-standard basis Symmetry and Structural Properties of Condensed Matter ed T Lulek, B Lulek and A Wal (Singapore: World Scientific)
71. Kibler M R 2006 Int. J. Mod. Phys. B 20 1792
72. Kibler M R and Planat M 2006 Int. J. Mod. Phys. B 20 1802
73. Kibler M R 2007 SIGMA 3 092
74. Lévy-Leblond J-M 1973 Rev. Mex. Fís. 22 15
75. Vourdas A 1990 Phys. Rev. A 41 1653
76. Chaichian M and Ellinas D 1990 J. Phys. A: Math. Gen. 23 L291
77. Ellinas D 1991 J. Math. Phys. 32 135
78. Vourdas A 2004 Rep. Prog. Phys. 67 267
79. Fairlie D B, Fletcher P and Zachos C K 1990 J. Math. Phys. 31 1088
80. Daoud M, Hassouni Y and Kibler M 1998 The k-fermions as objects interpolating between fermions and bosons Symmetries in Science X ed B Gruber and M Ramek (New York: Plenum)
81. Ellinas D and Floratos E G 1999 J. Phys. A: Math. Gen. 32 L63
82. Delsarte P, Goethals J M and Seidel J J 1975 Philips Res. Rep. 30 91
83. Ivanović I D 1981 J. Phys. A: Math. Gen. 14 3241
84. Wootters W K and Fields B D 1989 Ann. Phys., NY 191 363
85. Calderbank A R, Cameron P J, Kantor W M and Seidel J J 1997 Proc. Lond. Math. Soc. 75 436
86. Sylvester J J 1883 C. R. Acad. Sci., Paris XCVII 1336
87. Morris A O 1967 Q. J. Math. 18 7
88. Morris A O 1968 Q. J. Math. 19 289
89. Kostrikin A I, Kostrikin I A and Ufnarovski V A 1981 Proc. Steklov Inst. Math. 158 105
90. Kostrikin A I, Kostrikin I A and Ufnarovski V A 1981 Sov. Math. Dokl. 24 292
91. Kostrikin A I, Kostrikin I A and Ufnarovski V A 1982 Sov. Math. Dokl. 25 2327
92. Kostrikin A I and Tiep P H 1994 Expositions Math. 15
93. Boykin P O, Sitharam M, Tiep P H and Wocjan P 2007 Quantum Inf. Comput. 7 371
94. Bengtsson I 2006 Preprint quant-ph/0610216
95. Weigert S and Wilkinson M 2008 Preprint 0802.0394