= Gauge-invariant condensate momentum
{title2=$\mathbf p_s=\hbar\nabla\theta-q\mathbf A$}
A pair field transforms as $\Psi\mapsto e^{iq\chi/\hbar}\Psi$ when $\mathbf A\mapsto\mathbf A+\nabla\chi$. Its phase gradient alone is gauge dependent; $\mathbf p_s=\hbar\nabla\theta-q\mathbf A$ is invariant. With $\phi\mapsto\phi-\partial_t\chi$, the temporal combination $\hbar\dot\theta+q\phi$ is also invariant. The supercurrent is $\mathbf j=q\rho_s\mathbf p_s/m_*$. A negative electronic pair charge is consistent with either sign of current once this convention is retained throughout.
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