# Difference between Gravitational and Matter Scalar Fields

In the context of Scalar-Tensor theories of gravity (for example in Brans-Dicke) what is the difference between gravitational and matter scalar Fields?

My doubt comes from "The scalar-tensor Theory of gravitation" of Y. Fujii and K. Maeda (pag. 68, near formula 3.34).

Clearly, a scalar field is a gravitational one in the Jordan frame if it's coupled to $R$ into the action. With a conformal transformation we can go to the Einstein frame, in which the (redefined) field is now coupled to matter. I guess that this is still a gravitational scalar field, because is derived from the first field.

So, it's correct to say that a field is a matter field if it's only in the matter part of the action in the Jordan frame? I think that this can be true, since Jordan frame is often called the "physical" one.

And in the Einstein frame? It seems to me that every scalar field coupled to matter can be transformed in a non-minimally coupled field into the Jordan frame.

• The "matter fields" (in fact the source of the gravitational field) are not scalar fields. Electrons and quarks are spin one half particles. If you consider radiation as source for the gravitational field, it is about spin $1$ particles... – Trimok Jul 16 '14 at 9:24
• We are speaking even about hypothetical matter scalar fields. Anyway, a concrete example is given by the Higgs field. – Rexcirus Jul 16 '14 at 11:30
• Anyway, it is up to you to decide what you put in the matter Lagrangian, for your particular model. So there is no problem to distinguish a hypothetic matter scalar field, and the $\Phi$ field used in a Brans-Dicke theory, which corresponds to a non-constant gravitationnal constant. Moreover, the trace of the matter stress-energy tensor acts as a source for this field $\Phi$, so the difference is clear. – Trimok Jul 17 '14 at 8:23