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Coupling Constant

  1. Jan 7, 2014 #1
    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. jcsd
  3. Jan 7, 2014 #2
    It depends on the definition. You can see that Wikipedia defines the coupling constant as [itex] \alpha_G = m_e / m_p [/itex], whereas normally you would call [itex] 1/m_p [/itex] as the coupling constant, as it's what's in front of the interaction term in the Lagrangian.
     
  4. Jan 7, 2014 #3
    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?
     
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