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1 Introduction View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server 1 TWENTY FIVE YEARS OF ASYMPTOTIC FREEDOM David J. Gross Institute For Theoretical Physics, UCSB Santa Barbara, California, USA e-mail: [email protected] Abstract th On the o ccasion of the 25 anniversary of Asymptotic Freedom, celebrated at the QCD Euorconference 98 on Quantum Chro dynamics, Montp ellier, July 1998, I describ ed the discovery of Asymptotic Freedom and the emergence of QCD. 1 INTRODUCTION Science progresses in a much more muddled fashion than is often pictured in history b o oks. This is esp ecially true of theoretical physics, partly b ecause history is written by the victorious. Con- sequently, historians of science often ignore the many alternate paths that p eople wandered down, the many false clues they followed, the many misconceptions they had. These alternate p oints of view are less clearly develop ed than the nal theories, harder to understand and easier to forget, esp ecially as these are viewed years later, when it all really do es make sense. Thus reading history one rarely gets the feeling of the true nature of scienti c development, in which the element of farce is as great as the element of triumph. The emergence of QCD is a wonderful example of the evolution from farce to triumph. During a very short p erio d, a transition o ccurred from exp erimental discovery and theoretical confusion to theoretical triumph and exp erimental con rmation. In trying to relate this story, one must be wary of the danger of the p ersonal bias that o ccurs as one lo oks back in time. It is not totally p ossible to avoid this. Inevitably, one is fairer to oneself than to others, but one can try. One can take consolation from Emerson, who said that \There is prop erly no history; only biography." 1 Talk delivered at the QCD Euorconference 98 on Quantum Chro dynamics, Montp ellier, July 1998 1 2 THE THEORETICAL SCENE Iwould like rst to describ e the scene in theoretical particle physics, as I saw it in the early 1960's at Berkeley, when I started as a graduate student. The state of particle physics was then almost the complete opp osite of to day. It was a p erio d of exp erimental supremacy and theoretical imp otence. The construction and utilization of ma jor accelerators were pro ceeding at full steam. Exp erimental discoveries and surprises app eared every few months. There was hardly any theory to sp eak of. The emphasis was on phenomenology, and there were only small islands of theoretical advances here and there. Field theory was in disgrace; S-Matrix theory was in full blo om. Symmetries were all the rage. The eld was divided into the study of the weak and the strong interactions. In the case of the weak interactions, there was a rather successful phenomenological theory, but not much new data. The strong interactions were where the exp erimental and theoretical action was, particularly at Berkeley. They were regarded as esp ecially unfathomable. The prevalent feeling was that it would takeavery long time to understand the strong interactions and that it would require revolutionary concepts. For a young graduate student this was clearly the ma jor challenge. The feeling at the time was well expressed by Lev Landau in his last pap er, called \Fundamental Problems," which app eared in a memorial volume to Wolfgang Pauli in 1959 [1] . In this pap er he argued that quantum eld theory had b een nulli ed by the discovery of the zero charge problem. He said: \It is well known that theoretical physics is at present almost helpless in dealing with the problem of strong interactions.... By now the nulli cation of the theory is tacitly accepted even by theoretical physicists who profess to dispute it. This is evident from the almost complete disapp earance of pap ers on meson theory and particularly from Dyson's assertion that the correct theory will not b e found in the next hundred years." Let us explore the theoretical milieu at this time. 2.1 QUANTUM FIELD THEORY Quantum eld theory was originally develop ed for the treatment of electro dynamics almost im- mediately after the completion of quantum mechanics and the discovery of the Dirac equation. It 2 seemed to b e the natural to ol for describing the dynamics of elementary particles. The application of quantum eld theory had imp ortant early success. Fermi formulated a powerful and accurate phenomenological theory of b eta decay, whichwas to serve as a framework for exploring the weak interactions for three decades. Yukawa prop osed a eld theory to describ e the nuclear force and predicted the existence of heavy mesons, which were so on discovered. On the other hand, the theory was confronted from the b eginning with severe diculties. These included the in nities that app eared as so on as one wentbeyond lowest order p erturbation theory,aswell as the lackof any non-p erturbative understanding of dynamics. By the 1950's the suspicion of eld theory had deep ened to the p oint that a p owerful dogma emerged{that eld theory was fundamentally wrong, esp ecially in its application to the strong interactions. The renormalization pro cedure, develop ed by Richard Feynman, Julian Schwinger, Sin-itiro Tomanaga and Freeman Dyson, was sp ectacularly successful in Quantum Electro dynamics. How- ever, the physical meaning of renormalization was not truly understo o d. The feeling of most was that renormalization was a trick. This was esp ecially the case for the pioneering inventors of quantum eld theory (for example Dirac and Wigner). They were prepared at the rst drop of an in nity to renounce their b elief in quantum eld theory and to brace for the next revolution. However it was also the feeling of the younger leaders of the eld, who had laid the foundations of p erturbative quantum eld theory and renormalization in the late '40's. The prevalent feeling was that renormalization simply swept the in nities under the rug, but that they were still there and rendered the notion of lo cal elds meaningless. To quote Feynman, sp eaking at the 1961 Solvay conference[2 ], \I still hold to this b elief and do not subscrib e to the philosophy of renormalization." Field theory was almost totally p erturbative at that time. The nonp erturbative techniques that had b een tried in the 1950's had all failed. The path integral, develop ed by Feynman in the late 1940's, which later proved so valuable for a nonp erturbative formulation of quantum eld theory as well as a to ol for semiclassical expansions and numerical approximations, was almost completely forgotten. In a sense the Feynman rules were to o successful. They were an immensely useful, picturesque and intuitiveway of p erforming p erturbation theory. However these alluring qualities also convinced many that all that was needed from eld theory were these rules. They diverted attention from the non-p erturbative dynamical issues facing eld theory. In my rst course on quantum eld theory at Berkeley in 1965, I was taught that Field Theory =Feynman Rules. 3 In the United States, the main reason for the abandonment of eld theory was simply that one could not calculate. American physicists are inveterate pragmatists. Quantum eld theory had not proved to b e a useful to ol with which to make contact with the explosion of exp erimental discoveries. The early attempts in the 1950's to construct eld theories of the strong interactions were total failures. In hindsight this was not surprising since a eld theory of the strong interactions faced two enormous problems. First, which elds to use? Following Yukawa, the rst attempts employed pion and nucleon elds. So on, with the rapid proliferation of particles, it b ecame evident that nothing was sp ecial ab out the nucleon or the pion. All the hadrons, the strange baryons and mesons as well as the higher spin recurrences of these, app eared to be equally fundamental. The obvious conclusion that all hadrons were comp osites of more fundamental constituents was thwarted by the fact that no matter how hard one smashed hadrons at each one had not b een able to lib erate these hyp othetical constituents. This was not analogous to the paradigm of atoms made of nucleons and electrons or of nuclei comp osed of nucleons. The idea of p ermanently b ound, con ned, constituents was unimaginable at the time. Second, since the pion-nucleon coupling was so large, p erturbative expansions were useless. All attempts at non-p erturbative analysis were unsuccessful. In the case of the weak interactions, the situation was somewhat b etter. Here one had an adequate e ective theory{the four fermion Fermi interaction, which could be usefully employed, using p erturbation theory to lowest order, to organize and understand the emerging exp erimental picture of the weak interactions. The fact that this theory was non-renormalizable meant that beyond the Born approximation it lost all predictive value. This disease increased the suspicion of eld theory. Yang-Mills theory, which had app eared in the mid 1950's was not taken seriously. Attempts to apply Yang-Mills theory to the strong interactions fo cused on elevating global avor symmetries to lo cal gauge symmetries. This was problematic since these symmetries were not exact. In addition non-Ab elian gauge theories apparently required massless vector mesons{clearly not a feature of the strong interactions.
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