IL NUOVO CIMENTO VoL. 57 A, N. 4 21 Giugno 1980 Transformation of a Non-Abelian Gauge Theory into an Abelian Gauge Theory. I. KHAN Department o] Physics, University of Riyad - Riyad, Saudi Arabia (ricevuto il 6 Maggio 1980) Summary. -- An example is given to show that non-Abelian gauge theories which are not asymptotically free can be transformed into Abelian gauge theories. Field theories with the Lagrangian invariant under a non-Abelian gauge group have been of considerable interest in elementary-particle physics. The Salam-Weinberg unified theory of weak and electromagnetic interactions (1) and the quuntum chromodynamics (2) (QCD) of quarks and gluons are two examples of non-Abelian gauge theories. A property of special interest is the short-distance behaviour of the constituents in these theories. In quantum chromodynamics the constituents (quarks and gluons) behave like free particles at short distances (3) (asymptotic freedom). This remarkable behaviour is, in fact, a strong argument for regarding QCD as the correct theory of strong- interaction phenomena in view of the observed scaling (4) in deep inelastic electron scattering which has been understood on the basis of a model of free constituents for the nucleon (parton model). On the other hand, in the Salam- (1) A. SALAmi: in Elementary Particle Physics: Relativistic Groups and Analyticity, edited by N. SVARTHOL~I(Stockholm, 1968), p. 367; S. W]~INB]~RG: Phys. Rev..bett., 19, 1264 (1967). (~-) See, for example, W. MARCIANO and H. PAG]~LS: Phys. Rep. C, 36, 137 (1978); 0. W. GREEI~B~,RG: Annu. Rev. Nucl. Sei., 28, 327 (1978). (a) H . D . POLITZER: Phys. Rev..Lett., 30, 1346 (1973); D. J. GRoss and F. WILCZEK: Phys. Rev. Zett., 30, 1343 (1973). (a) J. D. BJORK~N: Phys. Rev., 179, 1547 (1969). 472