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Small-x physics in perturbative QCD

We review the parton model and the Regge approach to the QCD description of the deep-inelastic $ep$ scattering at the small Bjorken variable $x$ and demonstrate their relation with the DGLAP and BFKL evolution equations. It is shown, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The conformal invariance of the BFKL pomeron in the impact parameter space is used to investigate the scattering amplitudes at high energies and fixed momentum transfers. The remarkable properties of the Schrödinger equation for compound states of an arbitrary number of reggeized gluons in the multi-colour QCD are reviewed. The gauge-invariant effective action describing the gluon-Reggeon interactions is constructed. The known next-to-leading corrections to the QCD pomeron are discussed.