Regular gauge slice
= Regular gauge slice
A gauge condition $F(x)=0$ is regular at a representative $x_0$ if its derivative along the <gauge orbit> is an invertible <matrix>. The <inverse function theorem> then makes the gauge-condition values valid local coordinates along that orbit. A unique zero without this regularity is insufficient: the translation action on the line with $F(x)=x^3$ has a unique zero but a zero derivative there. Multiple regular intersections give a <Gribov ambiguity> rather than a globally unique slice.