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

Gauge Boson Propagators in Spontaneously Broken Gauge Theories

  1. Oct 5, 2008 #1
    The propagator for gauge bosons in a spontaneously broken (non-abelian) gauge theory in the [itex]R_\xi[/itex] gauge is (see Peskin and Schroeder eqn. 21.53)

    [tex]
    \tilde{D}^{\mu\nu}_F(k)^{ab}=\frac{-i}{k^2-M^{ab}}\left[g^{\mu\nu}-(1-\xi)\frac{k^\mu k^\nu}{k^2-\xi M^{ab}}\right]\,,
    [/tex]​

    where [itex]M^{ab}[/itex] is the gauge boson mass matrix, and [itex]\xi[/itex] is the gauge fixing parameter. The matrices in the denominator should be interpreted as matrix inverses. To make perturbative calculations, I am supposed to diagonalize the mass matrix [itex]M^{ab}[/itex], and write the propagator in terms of the eigenvalues.

    I would like to make my calculations as general as possible, and avoid having to go to a particular model to diagonalize the mass matrix. Is there a way to rationalize the propagator above so that the matrices are in the numerator?
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted