Consider a classical scalar-tensor theory (I'm following this paper)

\begin{equation} S=\int d^4x\sqrt{-g}\left( \frac{1}{2\kappa^2}\mathcal{A}\left(\Phi\right)R -\frac{1}{2}\mathcal{B}\left(\Phi\right)\left(\nabla\Phi\right)^2 - V\left(\Phi\right) \right) + S_m\left[e^{2\alpha\left(\Phi\right)}g_{\mu\nu},\psi_m\right] \end{equation}

The Ricci scalar is $R$, the scalar field is $\Phi$, and $\psi_m$ are the ''matter fields''. The theory is said to be in the ''Einstein frame'' if $\mathcal{A}=1,\mathcal{B}=1$, and is said to be in the ''Jordan frame'' if $\alpha=0,\mathcal{B}=1$.

My question is: what is the origin of this terminology? It looks like the term ''Einstein frame'' was introduced by Hawking, but I can't figure out where the first paper where ''Jordan frame'' was coined (in Hawking's paper he calls it the ''Brans-Dicke frame'').



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