This represents an infinite number of constraints one for each value of formula_11. These come about from re-expressing General relativity as an formula_12 Yang–Mills type gauge theory (Yang–Mills is a generalization of Maxwell's theory where the gauge field transforms as a vector under Gauss transformations, that is, the Gauge field is of the form formula_13 where formula_14 is an internal index. See Ashtekar variables). These infinite number of Gauss gauge constraints can be "smeared" by test fields with internal indices, formula_15,