I have two questions, both relating to the SSB of Electroweak Lagrangian.

My notes say that after breaking and expanding around the VEV, the masses of $W$ and $Z$ are identified by comparing to the lagrangian

$$ L = m_{w}W^+_\mu W^{-\mu} + {\frac{1}{2}}mZZ. $$

My first question is why the factor of half for the case of the $Z$ bosons mass?

My other question is how the transformation to the unitary gauge

$$ \phi = \frac{1}{\sqrt{2}}(\frac{0}{v + H(x)}) $$ explicitly works, as in what does the transformation from the complex Higgs Doublet actually look like. Most texts I can find just state it, but I'm not sure how the process works.

  • 1
    $\begingroup$ The first question (v2) is a duplicate of physics.stackexchange.com/q/525913/2451 $\endgroup$
    – Qmechanic
    Nov 5, 2023 at 8:58
  • $\begingroup$ Thanks @Qmechanic, so from this can I interpret the factor 1/2 associated with a real field, also arising for a complex field but is absorbed in the definition of it (the factor of $\sqrt{2})$? $\endgroup$
    – Blazeboy01
    Nov 5, 2023 at 9:47
  • $\begingroup$ You are completely and unequivocally comfortable with the abelian case and cannot generalize it to the non-abelian one? Several good texts do detail it. $\endgroup$ Nov 6, 2023 at 13:33


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