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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)

    \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]\,,

    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
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