  In this ground braking paper, as well as in (Weyl (1929c,d)), Weyl  explicitly abandons his earlier attempt to unify electromagnetism  with the theory of general relativity. In his early attempt he  associated the electromagnetic vector potential  \(A_{j}(x)\) with the additional connection  coefficients that arise when a conformal structure is reduced to a  Weyl structure (see §4.1). The important concept of gauge  invariance, however, is preserved in his 1929 paper. Rather than  associating gauge transformations with the scale or gauge of the  spacetime metric tensor, Weyl now associates gauge transformations  with the phase of the Dirac spinor field \(\psi\) that represents  matter. In the introduction of (Weyl (1929b)), which presents in  detail the new formalism, Weyl describes his reinterpretation of the  gauge principle as follows: 