The photon-photon interaction at low x in the theory of reggeized gluons with a running coupling and Nc → ∞

The forward elastic amplitude for scattering of real and weakly virtual photons is studied in the framework of the theory of reggeized gluons, with large Nc and a running coupling constant introduced in the manner which preserves the bootstrap condition. Transition from a single to multiple pomeron exchanges is observed as x gets smaller. For very low x the amplitude acquires an eikkonal form. The photon structure function reveals a strong violation of scaling: it grows a Q2. As a function of x it behaves as (ln(1x)ln ln(1x))2. Correspondingly the cross-section for physical photons grows with energy as (ln s ln ln s)2. Hadronic structure functions and cross-sections are also briefly discussed.