Gauge theory for the Poincaré group

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.