  We extend the twistor string theory inspired formalism introduced in
hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory
to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel
representation of the gauge theory amplitudes as dispersion integrals, which
are surprisingly simple to evaluate. As an application we calculate one-loop
maximally helicity violating (MHV) scattering amplitudes with an arbitrary
number of external legs. The result we obtain agrees precisely with the
expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon,
Dunbar and Kosower using the cut-constructibility approach.
