De Sitter Gauge Theory of Gravitation

概要

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A gauge theory of gravitation is formulated on the basis of the de Sitter group. A vierbein type field b_k^l and a Yang-Mills type field A^<ab>_m, which have 16 and 40 components, respectively, are introduced. A relation between the b_k^l and the A<ab>_m with one scalar parameter f is set up and only the field A^<ab>_m is regarded as the gauge field. It is shown that the vierbein field in the gauge theories of Utiyama, Kibble, Hayashi and Nakano is obtained from the field A^<ab>_m by contracting the de Sitter group to the Poincare group. Some prescription is shown to be necessary in order to obtain a gauge invariant Lagrangian density of the matter field which by the contraction is reduced to a reasonable Lagrangian denisity in the Poincare gauge theory. Restrictions on the parameter f are obtained by considering the group contraction and by considering the limit A^<ab>_m→0. Several possible choices for the f are given explicitly.
理論物理学刊行会の論文
1979-07-25