  The technique of one-loop calculations for the processes involving Reggeized
quarks is described in the framework of gauge invariant effective field theory
for the Multi-Regge limit of QCD, which has been introduced by Lipatov and
Vyazovsky. The rapidity divergences, associated with the terms enhanced by
$\log (s)$, appear in the loop corrections in this formalism. The covariant
procedure of regularization of rapidity divergences, preserving the gauge
invariance of effective action is described. As an example application, the
one-loop correction to the propagator of Reggeized quark and $\gamma Q
q$-scattering vertex are computed. Obtained results are used to construct the
Regge limit of one-loop $\gamma\gamma\to q\bar q$ amplitude. The cancellation
of rapidity divergences and consistency of the effective field theory
prediction with the full QCD result is demonstrated. The rapidity
renormalization group within the effective field theory is discussed.
