We present a numerical model study of the zero-temperature infrared optical
properties of (III,Mn)V diluted magnetic semiconductors. Our calculations
demonstrate the importance of treating disorder and interaction effects
simultaneously in modelling these materials. We find that the conductivity has
no clear Drude peak, that it has a broadened inter-band peak near 220 meV, and
that oscillator weight is shifted to higher frequencies by stronger disorder.
These results are in good qualitative agreement with recent thin film
absorption measurements. We use our numerical findings to discuss the use of
f-sum rules evaluated by integrating optical absorption data for accurate
carrier-density estimates.Comment: 7 pages, 3 figure