Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I The propagator of the gauge field

  1. Jan 22, 2017 #1

    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. jcsd
  3. Jan 22, 2017 #2


    User Avatar
    Science Advisor
    Homework Helper

    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.
  4. Jan 22, 2017 #3
    Ok, I'm asking how to do so, or please mention a good reference for ..
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted