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## Main Question or Discussion Point

Dear all,

If we consider the lagrangian to have both geometric parts (Ricci scalar) and also a field, the action would take the form below:

\begin{equation}

S=\frac{1}{2\kappa}\int{\sqrt{-g} (\ R + \frac{1}{2} g^{\mu\nu} \partial_\mu \phi \partial_\nu \phi -V(\phi)\ )}

\end{equation}

which are the Einstein-Hilbert, the kinetic and the potential term respectively.

About the dimensions \begin{equation} [R]=L^{-2}\end{equation}, which is of course the curvature, so the other terms must have the same dimension.

How is this possible?

aren't they energy terms?

don't they have dimension of energy?!!!

If we consider the lagrangian to have both geometric parts (Ricci scalar) and also a field, the action would take the form below:

\begin{equation}

S=\frac{1}{2\kappa}\int{\sqrt{-g} (\ R + \frac{1}{2} g^{\mu\nu} \partial_\mu \phi \partial_\nu \phi -V(\phi)\ )}

\end{equation}

which are the Einstein-Hilbert, the kinetic and the potential term respectively.

About the dimensions \begin{equation} [R]=L^{-2}\end{equation}, which is of course the curvature, so the other terms must have the same dimension.

How is this possible?

aren't they energy terms?

don't they have dimension of energy?!!!

Last edited: