Applications of the renormalization group to high-energy physics

A phenomenological description of deep inelastic scattering is given, discussing the parton picture of hadrons and the experimental situation. The operator product expansion, the requisite tool for the analysis of the short distance structure of products of currents is discussed. It is shown how deep inelastic scattering probes current products on the light cone. The relevant twist-two operators and how they are separated from the structure functions are discussed. The renormalization group equations are derived using the minimal subtraction procedure of dimensional regularization. The fixed point structure of a general quantum field theory is discussed and it is proven that only non-Abelian gauge theories can be asymptotically free. The ultraviolet fixed point of gauge theories with fermions and scalar mesons is also analysed in detail. The author applies the general tools developed to the discussion of deep inelastic scattering, and presents the argument that Bjorken scaling implies asymptotic freedom. A description of the structure of AFGT, speculations about the low-energy dynamics of such a theory and the possibility of quark confinement and dynamical symmetry breaking are given. The application of asymptotic freedom to deep inelastic scattering and e+e- annihilation is described and the problem of weak radiative corrections briefly discussed. A general description is given of dynamical symmetry breaking, its relation to asymptotic freedom as well as a specific field theoretic realization. (Auth.)