 Gauge-coupling sign in Ginzburg-Landau superconductivity

For energy with kinetic term ${\hslash }^2|D_{\eta }\psi {|}^2/(2m)$, $\eta =\pm 1$, variation gives $-{\hslash }^2{D}_{\eta }^2\psi /(2m)+(\alpha +\beta |\psi {|}^2)\psi =0$ and current $j=\eta q\hslash \mathrm{Im}({\psi }^{\ast }\nabla \psi )/m-q^2|\psi {|}^{2}A/m$. Thus changing the sign of the covariant derivative changes the phase-gradient term of the current. The displayed energy, field equation and current must use the same convention.