Gauge theory for the Poincar\'e group
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 381-387
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TMF_1983_54_3_a5,
author = {M. O. Katanaev},
title = {Gauge theory for the {Poincar\'e} group},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {381--387},
publisher = {mathdoc},
volume = {54},
number = {3},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a5/}
}
M. O. Katanaev. Gauge theory for the Poincar\'e group. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 3, pp. 381-387. http://geodesic.mathdoc.fr/item/TMF_1983_54_3_a5/