Scaling and Conformal Field Theories

Take a region of a plane and rotate it about an axis to get a three-dimensional object as in Fig. 78 . If the length along the axis is L , then we would guess that the volume of the resulting object is \approx L^3 , with some O(1) constant of proportionality. This could be wrong if the shape is pathological or degenerate, but it is generally correct.