In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions to argue that it should appear in nature. The basic idea behind its plausibility is that local scale invariant theories have their currents given by T μ μ ν ν ξ ξ ν ν where ξ ξ ν ν is a Killing vector and T μ μ ν ν is a conserved operator (the stress-tensor) of dimension exactly d . For the associated symmetries to include scale but not conformal transformations, the trace T μ μ μ μ has to be a non-zero total derivative implying that there is a non-conserved operator of dimension exactly d − − 1 .