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Prog. Theor. Phys. Vol. 99 No. 3 (1998) pp. 327-336
Galilei Covariance and (4,1)-de Sitter Space
A. E. Santana,*,**
F. C. Khanna**,*** and
Y. Takahashi**
*Instituto de Fisica, Universidade Federal da Bahia
Campus de Ondina, 40210-340, Salvador, Bahia, Brazil
**Theoretical Physics Institute, Dept. of Physics, Univ. of Alberta
Edmonton, AB T6G 2J1, Canada
***TRIUMF, 4004, Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
(Received December 4, 1997)
Abstract:
A vector space G is introduced such that the Galilei
transformations are considered linear
mappings in this manifold. The
covariant structure of the Galilei Group (Y. Takahashi, Fortschr.
Phys. 36 (1988), 63, 83) is derived and the tensor
analysis is developed. It is
shown that the Euclidean space is embedded in the
(4,1)-de Sitter space through G. This is an interesting
and useful property, in particular, for the analysis carried out for
the Lie algebra of the
generators of linear transformations in G.
URL :
http://ptp.ipap.jp/link?PTP/99/327/
DOI : 10.1143/PTP.99.327
References:
- E. Inönü and E. P. Wigner, Nuovo Cim. 9 (1952), 705.
- V. Bargmann, Ann. Math. 59 (1954), 1.
- M. Hamermesh, Ann. of Phys. 17 (1960), 518.
-
L. Gagnon and P. Winternitz, J. of Phys. A21 (1988), 1493[IoP STACKS]; 22 (1989), 469, 499.
- W. I. Fushchich and A. G. Nikitin, Symmetries of Equations of Quantum Mechanics (Allerton Press, N.Y. 1994).
- A. Matos Neto, J.D. M. Vianna, A.E. Santana and F. C. Khanna, Phys. Essay 9 (1996), 596.
- Y. Takahashi, Fortschr. Phys. 36 (1988), 63.
- Y. Takahashi, Fortschr. Phys. 36 (1988), 83.
-
S. Malin, Phys. Rev. D9 (1974), 3228, [APS]and references quoted therein.
-
H. Bacry and J.-M. Levy-Leblond, J. Math. Phys. 9 (1968), 1605[CrossRef].
- M. Omote, S. Kamefuchi, Y. Takahashi and Y. Ohnuki, Fortschr. Phys. 37 (1989), 933.
- R. L. Bishop and S. I. Goldberg, Tensor Analysis on Manifolds (Dover Publ. N. York, 1980).
