Low-Energy Effective Action in N=4 Super Yang-Mills Theory

We consider N=4 supersymmetric Yang-Mills theory formulated in terms of N=2 superfields in harmonic superspace. Using the background field method we define manifestly gauge invariant and N=2 supersymmetric effective action depending on N=2 strength superfields and develop a general procedure for its calculation in one-loop approximation. Explicit form for this effective action is found for the case of SU(2) gauge group broken down to U(1).