respectively, where formula_56 is the field strength tensor of the connection formula_49 and where formula_58 is referred to as the vector constraint. The above-mentioned local in space rotational invariance is the original of the formula_46 gauge invariance here expressed by the Gauss law. Note that these constraints are polynomial in the fundamental variables, unlike as with the constraints in the metric formulation. This dramatic simplification seemed to open up the way to quantizing the constraints. (See the article Self-dual Palatini action for a derivation of Ashtekar's formalism).