Bjorken Limit in Perturbation Theory

We present detailed calculations illustrating the breakdown of the Bjorken limit in perturbation theory, in the "gluon" model of strong interactions. To second order in the gluon-ferrmion coupling constant in the scalar, pseudoscalar, and vector coupling models, we calculate the Bjorken-limit commutator of a pair of currents of arbitrary (vector, axial-vector, scalar, pseudoscalar, tensor) type. To fourth order in the coupling, in the scalar- and pseudoscalar-gluon models, we determine the leading logarithmic behavior of the SU₃-antisymmetric part of the vector-vector commutator. In the body of the paper we present the main results and discuss their various features and implications. The computational details are relegated to two appendices.