Dynamical Gauge Boson and Strong-Weak Reciprocity

It is proposed that asymptotically nonfree gauge theories are consistentlyinterpreted as theories of composite gauge bosons. It is argued that whenhidden local symmetry is introduced, masslessness and coupling universality ofdynamically generated gauge boson are ensured. To illustrate these ideas wetake a four dimensional Grassmannian sigma model as an example and show thatthe model should be regarded as a cut-off theory and there is a criticalcoupling at which the hidden local symmetry is restored. Propagator and vertexfunctions of the gauge field are calculated explicitly and existence of themassless pole is shown. The beta function determined from the $ Z $ factor ofthe dynamically generated gauge boson coincides with that of an asymptoticnonfree elementary gauge theory. Using these theoretical machinery we constructa model in which asymptotic free and nonfree gauge bosons coexist and theirrunning couplings are related by the reciprocally proportional relation.Comment: 19 pages, latex, 6 eps figures, a numbers of corrections are made in the tex