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 TMF, 1983, Volume 54, Number 3, Pages 381–387 (Mi tmf2129)

Gauge theory for the Poincaré group

M. O. Katanaev

Abstract: 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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English version:
Theoretical and Mathematical Physics, 1983, 54:3, 248–252

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Document Type: Article

Citation: M. O. Katanaev, “Gauge theory for the Poincaré group”, TMF, 54:3 (1983), 381–387; Theoret. and Math. Phys., 54:3 (1983), 248–252

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. O. Katanaev, “Linear connection in theories of Kaluza–Klein type”, Theoret. and Math. Phys., 56:2 (1983), 795–798
2. M. O. Katanaev, “Kinetic term for the Lorentz connection”, Theoret. and Math. Phys., 65:1 (1985), 1043–1050
3. M. O. Katanaev, “Kinetic part of dynamical torsion theory”, Theoret. and Math. Phys., 72:1 (1987), 735–741
4. Yu. N. Obukhov, I. V. Yakushin, “Experimental bounds on parameters of spin-spin interaction in gauge theory of gravitation”, Theoret. and Math. Phys., 90:2 (1992), 209–213
5. M. O. Katanaev, “Wedge Dislocation in the Geometric Theory of Defects”, Theoret. and Math. Phys., 135:2 (2003), 733–744
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