The propagator of the gauge field

[Monaliza Smile]

Hi,

I read in a QFT book that the free massive vector boson Lagrangian is

$\mathcal{L}_W = - \frac{1}{4} (\partial_\mu W^\dagger_\nu - \partial_\nu W_\mu^\dagger ) (\partial^\mu W^\nu - \partial^\nu W^\mu ) + M^2_W W^\dagger_\mu W^\mu$

gives the propagator in momentum space by:

$i \Delta_{\mu\nu} = - i \frac{g_{\mu\nu - k_\mu k_\nu/M^2_W}}{k^2-M^2_W}$

Any help how to derive the formula of the propagator from the Lagrangian ?

 

[dextercioby]

This is standard textbook material. The propagator is the unconnected two point Green function. To obtain Green functions from the action you need to apply the textbook formula and then switch to momentum representation via a Fouriert transformation of the propagator in the coordinate representation.

 

[Monaliza Smile]

Ok, I'm asking how to do so, or please mention a good reference for ..