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.Comment: Late

Weak measurement og the composite Goo-Haenchen shift in the critical region

By using a weak measurement technique, we investigated the interplay between the angular and lateral Goos-Haenchen shift of a focused He-Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos-Haenchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.Comment: 10 pages, 3 figure