This paper fills in some gaps in the Physical Theory of Diffraction (PTD). Possible extensions of the notion of the uniform and nonuniform currents are discussed for scattering problems involving objects with complex shapes and complex material properties. In the case of a perfectly conducting wedge, exact expressions for the nonuniform (fringe) current are presented in terms of fast convergent integrals. Their analytical properties are investigated in details. These integrals together with asymptotic expressions provide an efficient tool for numerical calculations of the nonuniform current. The results can be used for example in the analysis of scattering and antenna problems for large polyhedrons.