= Canonical Abelian Higgs shift
{title2=$\phi=(v+h+ib)/\sqrt2$}
For $\phi=\kappa(v+h+ib)$, the real fluctuation <kinetic terms> are $-\kappa^2[(\partial h)^2+(\partial b)^2]$. The same $v$ labels a <Minimum> of $V=\lambda(|\phi|^2-v^2/2)^2/4$ and gives <Canonical field normalization>[canonically normalized] real fields exactly when $\kappa^2=1/2$. This condition also makes $G=\partial\cdot A-\xi gvb$ cancel the gauge-scalar derivative mixing: its coefficient is $(2\kappa^2-1)gvA\cdot\partial b$. Changing the <normalization> of the fields without changing the <Gauge fixing>[gauge function] need not be a conventional diagonal $R_\xi$ gauge.
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