High Quality Content by WIKIPEDIA articles! In theoretical physics, by anomaly one usually means that the symmetry remains broken when the symmetry-breaking factor goes to zero. When the symmetry which is broken is scale invariance, then true power laws usually cannot be found from dimensional reasoning like in turbulence or quantum field theory. In the latter, the anomalous scaling dimension of an operator is the contribution of quantum mechanics to the classical scaling dimension of that operator. The classical scaling dimension of an operator O is determined by dimensional analysis from the Lagrangian (in 4 spacetime dimensions this means dimension 1 for elementary bosonic fields including the vector potentials, 3/2 for elementary fermionic fields etc.). However if one computes the correlator of two operators of this type, one often finds logarithmic divergences arising from one-loop Feynman diagrams. The expansion in the coupling constant has the schematic form

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