Note on scaling arguments in the effective average action formalism

The effective average action (EAA) is a scale-dependent effective action where a scale k is introduced via an infrared regulator. The k dependence of the EAA is governed by an exact flow equation to which one associates a boundary condition at a scale mu. We show that the mu dependence of the EAA is controlled by an equation fully analogous to the Callan-Symanzik equation which allows one to define scaling quantities straightforwardly. Particular attention is paid to composite operators which are introduced along with new sources. We discuss some simple solutions to the flow equation for composite operators and comment on their implications in the case of a local potential approximation.