# I The propagator of the gauge field

1. Jan 22, 2017

### 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 ?

2. Jan 22, 2017

### 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.

3. Jan 22, 2017

### Monaliza Smile

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