which is a one-form which takes on values in the Lie algebra of the translational Abelian group R, whence it is gauge invariant. But what does this mean? x = ξ (p) is a local section of the (pure translational) affine internal bundle M → M, another important structure in addition to the translational gauge field B μ. Geometrically, this field determines the origin of the affine spaces; it is known as Cartan ’s radius vector. In the gauge-theoretic framework, the one-form