As opposed to a recent claim that Weyl’s gauge field has a negative energy density, it is shown that the gauge field has a positive energy density, thus having a normal behaviour. Furthermore, Weyl’s gauge field is shown to interact with a special kind of spin-1/2 non-canonical spinor field, while a previous paper shows that it does not couple to a spin-1/2 canonical spinor field. It is, however, found that Weyl’s gauge field cannot have such a universal geometrical nature at all as the gravitational field gµν has, contrary to the original Weyl’s intention.
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Hayashi et al. (1979) studied this question.