Higher-order corrections in the cut-vertex formalism

An algorithm is given for the calculation of higher-order corrections to the cut vertices and their coefficient functions of deep-inelastic and annihilation processes in the model field theory ${\left({\Phi }^3\right)}_6$. The introduction of covariant phase-space variables renders the calculation simple and elucidates the relations between the deep-inelastic and annihilation structure functions.