Gauge theory of Poincaré symmetry

Abstract

The Einstein-Cartan theory of gravitation is shown to be the unique gauge theory of Poincar\'e symmetry as far as one chooses the Lagrangian to be the lowest possible combination in field strengths. Kibble's derivation of the theory is reformulated and refined in the fiber-bundle picture. The gauge potentials of the Lorentz subgroup are identified as the local affine-connection coefficients which in general allow torsion, and the field strengths of this subgroup are identified as the curvature tensor of the corresponding Riemann-Cartan geometry. The spin current of fermion fields creates the torsion of the geometry.