Geodesic
Gauge theory for the Poincaré group
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 381-387 Cet article a éte moissonné depuis la source Math-Net.Ru

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The method of constructing Lagrangians proposed by Cho [1] is generalized to the case of the Poincaré group. For this purpose, a nondegenerate right-invariant Riemannian metric is constructed for the Poincar6 group; this metric is leftinvariant with respect to the direct product of the Lorentz group and the subgroup of displacements. In a left-invariant basis, the metric depends nontrivially on the coordinates of the displacement subgroup, which leads to the appearance in the theory of a vector field. Using this vector field and gauge fields, one can introduce a tetrad field on the space-time manifold. After the Lorentz connection has been made compatible with the linear connection, the Lagrangian of the gauge fields of the Poincaré group reduces to a sum of invariants constructed from the curvature and torsion tensors plus a cosmological term. In the large-scale limit, the equations of motion become identical to Einstein's free equations. 
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     author = {M. O. Katanaev},
     title = {Gauge theory for the {Poincar\'e} group},
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M. O. Katanaev. Gauge theory for the Poincaré group. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 381-387. http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a5/

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