# Coupling Constant

1. Jan 7, 2014

### latentcorpse

Perhaps I'm confusing two different things but I've read online (http://en.wikipedia.org/wiki/Gravitational_coupling_constant) that the gravitational coupling constant is dimensionless and proportional to Newton's constant G.

However, I have also read that the gravitational coupling constant is proportional to the square root of G, and since in a 4d theory, G has mass dimension -2 (can see from an Einstein Hilbert action), the coupling will have dimension -1 and this is the reason GR can't be renormalised.

My questions are:

1, Which of these are correct?

2, How do we derive the relationship between the coupling and G?

Thanks.

2. Jan 7, 2014

### clamtrox

It depends on the definition. You can see that Wikipedia defines the coupling constant as $\alpha_G = m_e / m_p$, whereas normally you would call $1/m_p$ as the coupling constant, as it's what's in front of the interaction term in the Lagrangian.

3. Jan 7, 2014

### latentcorpse

Ok. Well now the 2nd definition makes sense. How can we see nonrenormalizability in the first case, where we have a dimensionless coupling? Presumably we need a different argument - looking at the superficial degree of divergence or something?