  We study the frequency dependencies of the fermion and photon dressing
functions in dynamical gap generation in graphene. We use a low energy
effective QED-like description, but within this approximation, we include all
frequency dependent effects including retardation. We obtain the critical
coupling by calculating the gap using a non-perturbative Dyson-Schwinger
approach. Compared to the results of our previous calculation [1] which used a
Lindhard screening approximation instead of including a self-consistently
calculated dynamical screening function, the critical coupling is substantially
reduced.
