Here Ω Ω ( x ) and R ( x ) are the scale factor and rotation that are associated to the conformal transformation f . The representation ρ ρ is trivial in the case of scalar fields, which transform as π π f ( O ) ( x ) = Ω Ω ( x ′ ) − − Δ Δ O ( x ′ ) . For vector fields, the representation ρ ρ is the fundamental representation, and we would have π π f ( O μ μ ) ( x ) = Ω Ω ( x ′ ) − − Δ Δ R μ μ ν ν ( x ′ ) O ν ν ( x ′ ) .