Removing Extraneous Factors from Einstein Action

[praharmitra]

I have an action of the form
$$\int \alpha \sqrt{g} R$$
where $\alpha$ is a field.
I want to do some kind of coordinate transformation, so that this term in the action becomes
$$\int \sqrt{g}R + \sqrt{g}(...)$$
where (...) consists of terms containing \alpha.

So basically, I want to remove $\alpha$ from the coefficient of R and move it to other terms in the lagrangian. Now, I know that this can be done! (I remember this from long ago), but for heaven's sake can't figure out how!

Can anyone tell me? Just a reference would be fine.

 

[Sam Gralla]

You probably want a field redefinition, not a coordinate transformation. I'd look up "Jordan frame" and "Einstein Frame" in "Brans Dicke Theory" (which contains an action like the one you write).

 

[praharmitra]

You probably want a field redefinition, not a coordinate transformation. I'd look up "Jordan frame" and "Einstein Frame" in "Brans Dicke Theory" (which contains an action like the one you write).

Yes. That's exactly what I wanted. Thanks a lot Sam. However, it turns out that this process cannot be done in 2 dimensions which is what I am working in.

Anyway thanks a lot for your help.