Asymptotic Freedom and QCD–A Historical Perspective

Nuclear Physics B (Proc. Suppl.) 135 (2004) 193–211 www.elsevierphysics.com Asymptotic Freedom and QCD–a Historical Perspective David J. Grossa aKavli Institute for Theoretical Physics, University of California, Santa Barbara CA 93106-4030, USA I describe the theoretical scene in the 1960’s and the developments that led to the discovery of asymptotic freedom and to QCD. 1. INTRODUCTION there was a rather successful phenomenological theory, but not much new data. The strong in- It was a pleasure to attend Loops and Legs in teractions were where the experimental and theo- Quantum Field Theory, 2004, and to deliver a his- retical action was, particularly at Berkeley. They torical account of the origins of QCD. The talks were regarded as especially unfathomable. The delivered at this exciting meeting are a dramatic prevalent feeling was that it would take a very illustration of how far QCD has developed since long time to understand the strong interactions its inception thirty years ago. Current and forth- and that it would require revolutionary concepts. coming experiments are performing tests of QCD For a young graduate student this was clearly the with amazing precision, and theoretical calcula- major challenge. The feeling at the time was well tions of perturbative QCD are truly heroic. In expressed by Lev Landau in his last paper, called particular it was especially satisfying for me to “Fundamental Problems,” which appeared in a meet at this conference some of the people, who memorial volume to Wolfgang Pauli in 1959 [1] . over the last 30 years have calculated the two, In this paper he argued that quantum field the- − three and four loop corrections to the β function ory had been nullified by the discovery of the zero that we calculated to one loop order 31 years ago. charge problem. He said: “It is well known that theoretical 2. THE THEORETICAL SCENE physics is at present almost helpless in I would like first to describe the scene in the- dealing with the problem of strong in- oretical particle physics, as I saw it in the early teractions.... By now the nullification 1960’s at Berkeley, when I started as a graduate of the theory is tacitly accepted even student. The state of particle physics was then by theoretical physicists who profess almost the complete opposite of today. It was a to dispute it. This is evident from the period of experimental supremacy and theoretical almost complete disappearance of pa- impotence. The construction and utilization of pers on meson theory and particularly major accelerators were proceeding at full steam. from Dyson’s assertion that the cor- Experimental discoveries and surprises appeared rect theory will not be found in the every few months. There was hardly any theory next hundred years.” to speak of. The emphasis was on phenomenol- Let us explore the theoretical milieu at this time. ogy, and there were only small islands of theoretical advances here and there. Field theory was 2.1. Quantum field theory in disgrace; S-Matrix theory was in full bloom. Quantum field theory was originally developed Symmetries were all the rage. The field was di- for the treatment of electrodynamics almost im- vided into the study of the weak and the strong mediately after the completion of quantum me- interactions. In the case of the weak interactions, chanics and the discovery of the Dirac equation. 0920-5632/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2004.09.049 194 D.J. Gross / Nuclear Physics B (Proc. Suppl.) 135 (2004) 193–211 It seemed to be the natural tool for describ- semiclassical expansions and numerical approx- ing the dynamics of elementary particles. The imations, was almost completely forgotten. In application of quantum field theory had impor- a sense the Feynman rules were too successful. tant early success. Fermi formulated a power- They were an immensely useful, picturesque and ful and accurate phenomenological theory of beta intuitive way of performing perturbation theory. decay, which was to serve as a framework for ex- However these alluring qualities also convinced ploring the weak interactions for three decades. many that all that was needed from field theory Yukawa proposed a field theory to describe the were these rules. They diverted attention from nuclear force and predicted the existence of heavy the non-perturbative dynamical issues facing field mesons, which were soon discovered. On the theory. In my first course on quantum field theory other hand, the theory was confronted from the at Berkeley in 1965, I was taught that Field The- beginning with severe difficulties. These included ory = Feynman Rules. In the United States, the the infinities that appeared as soon as one went main reason for the abandonment of field theory beyond lowest order perturbation theory, as well was simply that one could not calculate. Ameri- as the lack of any non-perturbative understanding can physicists are inveterate pragmatists. Quan- of dynamics. By the 1950’s the suspicion of field tum field theory had not proved to be a useful theory had deepened to the point that a pow- tool with which to make contact with the explo- erful dogma emerged–that field theory was fun- sion of experimental discoveries. The early at- damentally wrong, especially in its application tempts in the 1950’s to construct field theories to the strong interactions. The renormalization of the strong interactions were total failures. In procedure, developed by Richard Feynman, Ju- hindsight this was not surprising since a field the- lian Schwinger, Sin-itiro Tomanaga and Freeman ory of the strong interactions faced two enormous Dyson, was spectacularly successful in Quantum problems. First, which fields to use? Following Electrodynamics. However, the physical mean- Yukawa, the first attempts employed pion and ing of renormalization was not truly understood. nucleon fields. Soon, with the rapid prolifera- The feeling of most was that renormalization was tion of particles, it became evident that noth- a trick. This was especially the case for the pi- ing was special about the nucleon or the pion. oneering inventors of quantum field theory (for All the hadrons, the strange baryons and mesons example Dirac and Wigner). They were prepared as well as the higher spin recurrences of these, at the first drop of an infinity to renounce their appeared to be equally fundamental. The obvi- belief in quantum field theory and to brace for the ous conclusion that all hadrons were composites next revolution. However it was also the feeling of of more fundamental constituents was thwarted the younger leaders of the field, who had laid the by the fact thatno matter how hard one smashed foundations of perturbative quantum field the- hadrons at each one had not been able to lib- ory and renormalization in the late ’40’s. The erate these hypothetical constituents. This was prevalent feeling was that renormalization simply not analogous to the paradigm of atoms made of swept the infinities under the rug, but that they nucleons and electrons or of nuclei composed of were still there and rendered the notion of local nucleons. The idea of permanently bound, con- fields meaningless. To quote Feynman, speaking fined, constituents was unimaginable at the time. at the 1961 Solvay conference [2], “I still hold to Second, since the pion-nucleon coupling was so this belief and do not subscribe to the philoso- large, perturbative expansions were useless. All phy of renormalization.” Field theory was almost attempts at non-perturbative analysis were un- totally perturbative at that time. The nonper- successful. In the case of the weak interactions, turbative techniques that had been tried in the the situation was somewhat better. Here one 1950’s had all failed. The path integral, devel- had an adequate effective theory–the four fermion oped by Feynman in the late 1940’s, which later Fermi interaction, which could be usefully em- proved so valuable for a nonperturbative formula- ployed, using perturbation theory to lowest order, tion of quantum field theory as well as a tool for to organize and understand the emerging experi- D.J. Gross / Nuclear Physics B (Proc. Suppl.) 135 (2004) 193–211 195 mental picture of the weak interactions. The fact and Pomeranchuk, a generation of physicists was that this theory was non-renormalizable meant forbidden to work on field theory. One might that beyond the Born approximation it lost all wonder why the discovery of the zero charge prob- predictive value. This disease increased the sus- lem did not inspire a search for asymptotically picion of field theory. Yang-Mills theory, which free theories that would be free of this disease. had appeared in the mid 1950’s was not taken The answer, I think, is twofold. First, many other seriously. Attempts to apply Yang-Mills theory theories were explored–in each case they behaved to the strong interactions focused on elevating as QED. Second, Landau and Pomeranchuk con- global flavor symmetries to local gauge symme- cluded, I think, that this problem was inherent in tries. This was problematic since these symme- any quantum field theory, that an asymptotically tries were not exact. In addition non-Abelian free theory could not exist. gauge theories apparently required massless vec- tor mesons–clearly not a feature of the strong in- 2.2. The bootstrap teractions. In the Soviet Union field theory was The bootstrap theory rested on two principles, under even heavier attack, for somewhat different both more philosophical than scientific. First, lo- reasons. Landau and collaborators, in the late cal fields were not directly measurable. Thus they 1950’s, studied the high energy behavior of quan- were unphysical and meaningless. Instead, one tum electrodynamics.

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