If this choice is made, then there is no longer any Lorentz gauge symmetry because the internal Minkowski space fiber —over each point of the spacetime manifold —belongs to a fiber bundle with the Abelian group R as structure group. However, a translational gauge symmetry may be introduced thus: Instead of seeing tetrads as fundamental, we introduce a fundamental R translational gauge symmetry instead (which acts upon the internal Minkowski space fibers affinely so that this fiber is once again made local) with a connection B and a "coordinate field" x taking on values in the Minkowski space fiber.