In a scale invariant quantum field theory, by definition each operator O acquires under a dilation x → → λ λ x a factor λ λ − − Δ Δ , where Δ Δ is a number called the scaling dimension of O . This implies in particular that the two point correlation function ⟨ ⟨ O ( x ) O ( 0 ) ⟩ ⟩ depends on the distance as ( x 2 ) − − Δ Δ . More generally, correlation functions of several local operators must depend on the distances in such a way that ⟨ ⟨ O 1 ( λ λ x 1 ) O 2 ( λ λ x 2 ) … … ⟩ ⟩ = λ λ − − Δ Δ 1 − − Δ Δ 2 − − … … ⟨ ⟨ O 1 ( x 1 ) O 2 ( x 2 ) … … ⟩ ⟩