论文信息 - GALILEI COVARIANCE AND (4,1)-DE SITTER SPACE

GALILEI COVARIANCE AND (4,1)-DE SITTER SPACE

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; 36 (1988) 83) is derived and the tensor analysis is developed. It is shown that the Euclidean space is embedded the (4,1) de Sitter space through in G. This is an interesting and useful aspect, in particular, for the analysis carried out for the Lie algebra of the generators of linear transformations in G.

A. Santana | F. Khanna | Y. Takahashi

[1] A. Santana,et al. The Tomita-Takesaki Representation of w∗-Algebras, Lie Groups, and Thermofield Dynamics , 1996 .

[2] W. I. Fushchich,et al. Symmetries of Equations of Quantum Mechanics , 1994 .

[3] Y. Takahashi,et al. Galilean Covariance and the Schrödinger Equation , 1989 .

[4] Yasushi Takahashi. Towards the Many-Body Theory with the Galilei invariance as a Gluide Part II , 1988 .

[5] R. Bishop,et al. Tensor Analysis on Manifolds , 1980 .

[6] V. Bargmann,et al. On Unitary ray representations of continuous groups , 1954 .

[7] E. Wigner,et al. Representations of the Galilei group , 1952 .