Elementary Particles and Weyl's Gauge Field
Kazunori Hayashi, Masahiro Kasuya, Takeshi Shirafuji · Progress of Theoretical Physics · 1977
In the conventional theory of the conformal transformation of the metric tensor, only tensor fields can be treated. A general theoretical framework is presented such that both tensor and spinor fields can be incorporated. We define a conformal transformation of a metric spinor, for which a spinor basis is invariant, and we also define a scale transformation of a spinor basis, for which a metric spinor is invariant. It is shown that a particular mixing of a conformal transformation and a scale transformation gives rise to the usual conformal transformation of the metric tensor. Furthermore, it is proven that Weyl's gauge field does not couple to any elementary particle of spin 1/2, quite independently of its conformal weight.