= Gauss law constraint in gauge theory
{c}
{title2=$D_iE_i=\rho$}
The time component of a gauge field's equation of motion constrains the spatial fields and their momenta. In a <Yang-Mills theory> it has the covariant form $D_iE_i=\rho$; its Abelian form is <Gauss's law>. Time-dependent <collective coordinates> of a <gauge-theory soliton> require a temporal gauge field, or an equivalent horizontal projection, that satisfies this constraint before the kinetic metric is read from the action.
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