Deriving Graviton Propagator from Linearized Lagrangian

[michael879]

Hi, I'm working with the free space linearized gravitation lagrangian and trying to derive the proper propagator for it. I have no problem doing this, the only problem is that my QFT makes a quick note of what form this should take and I'm off by a factor of 4. The flatspace metric terms matching the components of the contracted graviton fields are of the correct form, and there is a 1/k^2 factor. I'm getting an additional factor of 2 though, while my book has a factor of 1/2. 1/2 makes much more sense to me, since there are two propagator terms, so I feel like I'm doing something wrong. Can anyone confirm what the correct propagator is for me?

*edit* sorry, the lagrangian I am using is the quadratic terms from the weak field expansion of R/kappa

 

[Bill_K]

I assume you're getting the usual field equation G_μν = κT_μν, and the factor of ½ you're talking about is due to the fact that in first order G_μν = ½ ◻h_μν. Well, but that factor doesn't matter, does it? Because in any event the propagator is defined to be the solution of ◻h_μν = δ⁴(x-x'), and any factor of ½ goes into the coupling constant, which will be 2κ.