  Quantum field theories containing scalar fields with equal quantum numbers
allow for a mixed kinetic term in the Lagrangian. It has been argued that this
mixing must be taken into consideration when performing renormalization group
(RG) analyses of such a theory. However, from the fact that scalar kinetic
mixing does not correspond to a physical observable, we show that no extra
parameters need to be introduced. Using a toy model, we explicitly derive the
1-loop RG equations (RGEs) in three different renormalization schemes to
demonstrate how this issue can be dealt with. In schemes without kinetic
mixing, either the fields mix during renormalization to produce non-diagonal
anomalous dimensions or the RGEs explicitly depend on the scalar masses.
Finally, we show how the different schemes are related to each other by scale
dependent field redefinitions.
