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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Massive vector field from CG coefficients

Can you offer guidance or do you also need help?

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