PERSPECTIVE The discovery of asymptotic freedom and the emergence of QCD David J. Gross* Kavli Institute For Theoretical Physics, University of California, Santa Barbara, CA 93106-0430 he progress of science is much was divided into the study of the weak that a powerful dogma emerged—that more muddled than is depicted and the strong interactions, the two field theory was fundamentally wrong, in most history books. This is mysterious forces that operate within especially in its application to the strong especially true of theoretical the nucleus. In the case of the weak in- interactions. Tphysics, partly because history is written teractions, there was a rather successful The renormalization procedure, devel- by the victorious. Consequently, histori- phenomenological theory, but not much oped by R. Feynman, J. Schwinger, ans of science often ignore the many new data. The strong interactions were S. Tomanaga, and F. Dyson, which had alternate paths that people wandered where the experimental and theoretical eliminated the ubiquitous infinities that down, the many false clues they fol- action was, particularly at Berkeley. occurred in calculations by expressing lowed, the many misconceptions they They were regarded as especially unfath- physical observables in terms of physical had. These alternate points of view are omable. In hindsight, this was not parameters, was spectacularly successful in less clearly developed than the final the- surprising since nature was hiding her Quantum Electrodynamics (QED). How- ories, harder to understand and easier secrets. The basic constituents of had- ever, the physical meaning of renormaliza- to forget, especially as these are viewed rons (strongly interacting particles) were tion was not truly understood. The feeling years later, when it all really does make invisible. We now know that these are of most was that renormalization was a sense. Thus, reading history one rarely quarks, but no one had ever seen a trick. This was especially the case for the gets the feeling of the true nature of quark, no matter how hard protons were pioneering inventors of quantum field the- scientific development, in which the ele- smashed into protons. Furthermore, the ory. They were prepared at the first ap- ment of farce is as great as the element ‘‘color’’ charges we now know are the pearance of divergences to renounce their of triumph. source of the Chromodynamic fields, belief in quantum field theory and to The emergence of QCD is a wonder- the analogs of the electric charge, were brace for the next revolution. However, it ful example of the evolution from farce equally invisible. The prevalent feeling was also the feeling of the younger leaders to triumph. During a very short period, was that it would take a very long time of the field, who had laid the foundations a transition occurred from experimental to understand the nuclear force and that of perturbative quantum field theory and discovery and theoretical confusion to it would require revolutionary concepts. renormalization in the late 1940s. The theoretical triumph and experimental Freeman Dyson had asserted that ‘‘the prevalent feeling was that renormalization confirmation. In this Nobel lecture, I correct theory will not be found in the simply swept the infinities under the rug, shall describe the turn of events that led next hundred years.’’ For a young gradu- but that they were still there and rendered to the discovery of asymptotic freedom, ate student such as myself, this was the notion of local fields meaningless. To which in turn led to the formulation of clearly the biggest challenge. quote Feynman, speaking at the 1961 QCD, the final element of the remark- Solvay conference (1), ‘‘I still hold to this ably comprehensive theory of elemen- Quantum Field Theory belief and do not subscribe to the philoso- tary particle physics—the Standard Quantum field theory was originally phy of renormalization.’’ Model. I shall then briefly describe the developed for the treatment of Electro- Field theory was almost totally pertur- experimental tests of the theory and the dynamics, immediately after the com- bative at that time; all nonperturbative implications of asymptotic freedom. pletion of quantum mechanics and the techniques that had been tried in the discovery of the Dirac equation. It 1950s had failed. The path integral, de- Particle Physics in the 1960s seemed to be the natural tool for de- veloped by Feynman in the late 1940s, The early 1960s, when I started my scribing the dynamics of elementary par- which later proved so valuable for a graduate studies at UC Berkeley, were a ticles. The application of quantum field nonperturbative formulation of quantum period of experimental supremacy and theory to the nuclear forces had impor- field theory as well as a tool for semi- theoretical impotence. The construction tant early success. Fermi formulated a classical expansions and numerical ap- and utilization of major accelerators powerful and accurate phenomenologi- proximations, was almost completely were proceeding at full steam. Experi- cal theory of beta decay, which (al- forgotten. In a sense, the Feynman rules mental discoveries and surprises ap- though deficient at high energy) was to were too successful. They were an im- peared every few months. There was serve as a framework for exploring the hardly any theory to speak of. The em- weak interactions for three decades. *E-mail: [email protected]. phasis was on phenomenology, and Yukawa proposed a field theory to de- Adapted from Les Prix Nobel, 2004. © 2004 by the Nobel there were only small islands of theoret- scribe the nuclear force and predicted Foundation ical advances here and there. Field the- the existence of heavy mesons, which Editor’s Note: This article is a version of David Gross’ Nobel ory was in disgrace; S-Matrix theory was were soon discovered. On the other Lecture ‘‘The Discovery of Asymptotic Freedom and the in full bloom. Symmetries were all of hand, quantum field theory was con- Emergence of QCD.’’ The 2004 Nobel Price in Physics was the rage. Of the four forces observed in fronted from the beginning with severe awarded to Drs. Gross, Frank Wilczek, and H. David Politzer for their discovery of asymptotic freedom in the theory of nature, only gravity and electromagne- difficulties. These included the infinities the strong interaction. The Nobel Foundation graciously tism were well understood. The other that appeared as soon as one went be- has granted us permission to reprint this article. The Nobel two forces, the weak force responsible yond lowest order perturbation theory, Lectures provide examples of successful approaches to ma- for radioactivity and the strong nuclear as well as the lack of any nonperturba- jor scientific problems. However, in recent years, these lectures have rarely been read, perhaps because of the force that operated within the nucleus, tive tools. By the 1950s, the suspicion of difficulty in obtaining the collections. By reprinting this were largely mysterious. Particle physics field theory had deepened to the point lecture, we hope to broaden their exposure. www.pnas.org͞cgi͞doi͞10.1073͞pnas.0503831102 PNAS ͉ June 28, 2005 ͉ vol. 102 ͉ no. 26 ͉ 9099–9108 Downloaded by guest on September 28, 2021 mensely useful, picturesque, and intui- to apply Yang–Mills theory to the this property. But more importantly, I tive way of performing perturbation strong interactions focused on elevating think, dielectric screening is a natural theory. However, these alluring qualities global flavor symmetries to local gauge physical explanation of charge renormal- also convinced many that all that was symmetries. This was problematic, since ization, and they were unaware of any needed from field theory were these these symmetries were not exact. In simple physical reason for the opposite rules. They diverted attention from the addition, non-Abelian gauge theories effect. Thus, they assumed that the nonperturbative dynamical issues facing apparently required massless vector problem of zero charge would arise in field theory. In my first course on quan- mesons—clearly not a feature of the any field theory of the strong interac- tum field theory at Berkeley in 1965, I strong interactions. tion, but here it was an immediate ca- was taught that Field Theory ϭ Feynman In the Soviet Union, field theory was tastrophe. In the Soviet Union, this was Rules. Today, we know that there are under even heavier attack, for somewhat thought to be a compelling reason why many phenomena, especially confine- different reasons. Landau and collabora- field theory was wrong, and certainly ment in QCD, that cannot be under- tors, in the late 1950s, studied the high- inappropriate for the strong force. stood perturbatively. energy behavior of QED. They explored Landau decreed that ‘‘We are driven to In the United States, the main reason the relation between the physical elec- the conclusion that the Hamiltonian for the abandonment of field theory for tric charge and the bare electric charge method for strong interaction is dead the strong interactions was simply that as seen at infinitesimally small distances. and must be buried, although of course one could not calculate. American phys- The fact that the electric charge in QED with deserved honor’’ (4). icists are inveterate pragmatists. Quan- depends on the distance at which we Under the influence of Landau and tum field theory had not proved to be a measure it is due to ‘‘vacuum polariza- Pomeranchuk, a generation of physicists useful tool with which to make contact tion.’’ The vacuum, the ground state of was forbidden to work on field theory. with the explosion of experimental dis- a relativistic quantum mechanical sys- Why did the discovery of the zero coveries. The early attempts in the 1950s tem, should be thought of as a medium charge problem not inspire a search for to construct field theories of the strong consisting of virtual particles.