= Charge-constrained scalar-field scaling
{title2=$E_Q[f_\lambda]=\lambda^{2-d}T+\lambda^{-d}W+\lambda^dQ^2/(2I)$}
For $f_\lambda(x)=f(\lambda x)$ in $d$ space dimensions, write $T=\tfrac12\int|\nabla f|^2$, $W=\int U(f)$ and $I=\int f^2$. Eliminating the rotation frequency by $\omega=Q/I$ gives the displayed fixed-charge scaling. The positive-power charge term can balance the gradient and potential terms even for $d\ge3$. This evades the static <Derrick theorem> because the field is time-dependent and the relevant variations preserve its <Noether charge>.
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