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Title

Differential calculus on 'non-standard' (h-deformed) Minkowski spaces

Authors 1, 2

Affiliations

  1. Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, E-46100-Burjassot (Valencia), Spain
  2. Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E-46071 Valencia, Spain

Abstract

The differential calculus on 'non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.

Bibliography

  1. [1] J.A. de Azcárraga and F. Rodenas, J. Phys. A29, 1215 (1996).
  2. [2] E.E. Demidov, Yu. I. Manin, E.E. Mukhin and D.V. Zhadanovich, Progr. Theor. Phys. Suppl. 102, 203 (1990); M. Dubois-Violette and G. Launer, Phys. Lett. B245, 175 (1990); S. Zakrzewski, Lett. Math. Phys. 22, 287 (1991); S.L. Woronowicz, Rep. Math. Phys. 30, 259 (1991); B.A. Kupershmidt, J. Phys. A25, L1239 (1992); Ch. Ohn, Lett. Math. Phys. 25, 85 (1992).
  3. [3] H. Ewen, O. Ogievetsky and J. Wess, Lett. Math. Phys. 22, 297 (1991).
  4. [4] V. Karimipour, Lett. Math. Phys. 30, 87 (1994); ibid. 35, 303 (1995).
  5. [5] L.D. Faddeev, N. Yu. Reshetikhin and L.A. Takhtajan, Alg. i Anal. 1, 178 (1989) (Leningrad Math. J. 1, 193 (1990)).
  6. [6] Yu. I. Manin, Quantum groups and non-commutative geometry, CRM, Univ. Montréal (1988); Commun. Math. Phys. 123, 163 (1989); Topics in non-commutative geometry, Princeton Univ. Press (1991); J. Wess and B. Zumino, Nucl. Phys. (Proc. Suppl.) 18B, 302-312 (1990).
  7. [7] S.L. Woronowicz and S. Zakrzewski, Compositio Math. 94, 211 (1994).
  8. [8] P. Podleś and S. Woronowicz, Commun. Math. Phys. 178, 61 (1996).
  9. [9] P. Podleś and S. Woronowicz, Commun. Math. Phys. 130, 381 (1990).
  10. [10] U. Carow-Watamura, M. Schlieker, M. Scholl and S. Watamura, Z.Phys. C48, 159 (1990); Int. J. Mod. Phys. A6, 3081 (1991).
  11. [11] O. Ogievetsky, W.B. Schmidke, J. Wess and B. Zumino, Commun. Math. Phys. 150, 495 (1992).
  12. [12].
  13. [13] L. Freidel and J.M. Maillet, Phys. Lett. B262, 278 (1991).
  14. [14] P.P. Kulish and E.K. Sklyanin, J. Phys. A25, 5963 (1992).
  15. [15] P.P. Kulish and R. Sasaki, Progr. Theor. Phys. 89, 741 (1993).
  16. [16] Majid S., in Quantum Groups, Lect. Notes Math. 1510, 79 (1992); J. Math. Phys. 32, 3246 (1991).
  17. [17] S. Majid, J. Math. Phys. 34, 1176 (1993); Commun. Math. Phys. 156, 607 (1993).
  18. [18] B. Zumino, Introduction to the differential geometry of quantum groups, in Mathematical Physics X, K. Schmüdgen ed., Springer-Verlag (1992), p. 20.
  19. [19] J.A. de Azcárraga, P.P. Kulish and F. Rodenas, Lett. Math. Phys. 32, 173 (1994).
  20. [20] J.A. de Azcárraga and F. Rodenas, Differential calculus on q-Minkowski space, in Quantum groups, J. Lukierski et al. eds., PWN (1994), p. 221.
  21. [21] P. Podleś, Commun. Math. Phys. 181, 569 (1996).
  22. [22] O. Ogievetsky and B. Zumino, Lett. Math. Phys. 25, 131 (1992).
  23. [23] U. Meyer, Commun. Math. Phys. 168, 249 (1995); S. Majid and U. Meyer, Z. Phys. C63, 357 (1994).
  24. [24] A.P. Isaev and A.A. Vladimirov, Lett. Math. Phys. 33, 297 (1995).
Banach Center Publications
1997/40/1
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Pages:
351-360
Main language of publication
English
Published
1997
Exact and natural sciences