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Massive vector field from CG coefficients

  1. Jul 27, 2010 #1
    I'm currently reading Weinberg, see http://books.google.com/books?id=3ws6RJzqisQC&lpg=PA207&ots=Cu9twmTMTE&pg=PA207#v=onepage&q&f=false" for the relevant section.

    In §5.3, the coefficient functions at zero momentum (or polarisation vectors) are unique up to a Lorentz transformation and scale factor. Looking around, I've noticed a lot of other authors, Ryder for one, use (1,0,0,0), (0,1,0,0) and (0,0,1,0), which aren't related to Weinberg's vectors by a Lorentz transformation and scale factor. These are the same vectors you get if you use the Clebsch-Gordan coefficients as in §5.7 for a (1,0) field. The problem is the imaginary parts in Eq. (5.3.25). You can't even make all the vectors real up to a phase, to be absorbed by the normalisation.

    I'm also unsure how to pass from the pair of indices a,b to a single index l, but that's a different (though related) problem and shouldn't be an issue for the (1,0) representation where b only takes the value 0.

    Any light shed on this would be appreciated.
     
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
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