for any spatial diffeomorphism formula_277 on formula_151. To understand why one cannot define an operator for the quantum spatial diffeomorphism constraint consider what is called a 1-parameter subgroup formula_279 in the group of spatial diffeomorphisms, this is then represented as a 1-parameter unitary group formula_280 on formula_242. However, formula_280 is not weakly continuous since the subspace formula_283 belongs to and the subspace formula_275 belongs to are orthogonal to each other no matter how small the parameter formula_285 is. So one always has