Ultraviolet Behavior of Non-Abelian Gauge Theories

Non-Abelian gauge theories have received much attention recently as a means of constructing unified and renormalizable theories of the weak and electromagnetic interactions. ' In this note we report on an investigation of the ultraviolet (UV) asymptotic behavior of such theories. We have found that they possess the remarkable feature, perhaps unique among renormalizable theories, of asymptotically approaching free-field theory. Such asymptotically free theories will exhibit, for matrix elements of currents between on-mass-shell states, Bjorken scaling. We therefore suggest that one should look to a non-Abelian gauge theory of the strong interactions to provide the explanation for Bjorken scaling, which has so far eluded field-theoretic understanding. The UV behavior of renormalizable field theories can be discussed using the renormalization-group equations, "which for a theory involving one field (say gq') are [m&/em+ P(g) 8/Sg -ny(g)11",»~"i(g; P„... , P„)=0. (1)