Fundamental-doublet breaking of SU(2) (source code)

= Fundamental-doublet breaking of SU(2)
{title2=$m_A=gv/2,\ m_h^2=2\lambda v^2$}

A single <complex scalar field> in the two-dimensional <fundamental representation> with potential $\lambda(\phi^\dagger\phi-v^2/2)^2$, $\lambda,v>0$, has a three-sphere <vacuum manifold>. The stabilizer in $SU(2)$ of a chosen nonzero vector is trivial, so all three <gauge bosons> acquire the common <mass> $gv/2$. In <unitary gauge>, $\phi=(0,v+h)^T/\sqrt2$ leaves one physical radial scalar of squared <mass> $2\lambda v^2$. Its couplings are $g^2vhA^2/4+g^2h^2A^2/8-\lambda vh^3-\lambda h^4/4$. The three angular fields become longitudinal vector <polarizations> through the <Higgs mechanism>.