Research Profile

*by Roberto Lalli***David J. Gross ****Nobel Prize in Physics 2004 together with H. David Politzer and Frank Wilczek "for the discovery of asymptotic freedom in the theory of the strong interaction".**

David J. Gross is an eminent American theoretical physicist, known for his contribution to the discovery of the asymptotic freedom of the non-Abelian gauge field theory of strong interaction—a work that gained him the 2004 Nobel Prize in Physics. In collaboration with his PhD student Frank Wilczek, Gross demonstrated that Yang-Mills theories have the property of asymptotic freedom, i.e., have an effective coupling constant that goes to zero for short distances. This proof provided a new impetus towards the quantum field theoretic understanding of strong interactions. In a matter of months, the SU(3) colour Yang-Mills theory of strong interactions emerged from the work of several researchers. By the end of the 1970s, this theory had gained consensus and found a charming name: quantum chromodynamics (QCD). Following a series of experimental confirmations, QCD came to be accepted as the second pillar of the Standard Model of particle physics, the first being the SU(2)xU(1) gauge theory of electroweak interactions. After this discovery, Gross continued to be at the forefront of theoretical research in quantum field theory, high-energy physics, and quantum gravity. In the 1980s, Gross shifted his focus to the string theories of quantum gravity, becoming one of the major protagonists of the so-called ‘first superstring revolution’ because of his role in the formulation of the heterotic string theory.

**From USA to Israel and Return**

David Gross was born in Washington, D.C., on February 19, 1941, the eldest son in a family with a broad intellectual background. The father Bertram Myron Gross was an eminent American social scientist, whose best-known achievement was his collaboration with Democratic Party Senator James E. Murray in writing the Employment Act of 1946. His mother Nora (née Faine) majored in chemistry, but did not pursue a career in science. Gross’s partents both encouraged their four children to develop intellectual interests very early in their life.

In 1953, Gross moved with his family to Israel because his father was a member of an American advisory team sent to Israel by the Eisenhower administration. There, Gross began to be interested in mathematics and physics at the age of thirteen. Gross was fortunate to have high quality teachers during his secondary education. After graduation from high school, Gross pursued his studies in physics and mathematics at the Hebrew University, receiving his bachelor’s degree in 1962. Determined to become a theoretical physicist, Gross applied to several universities in the United States, and received a positive response from the University of California at Berkeley, where Gross began his PhD studies under the supervision of the American theoretical physicist Geoffrey Chew.

At that time, the Berkeley setting was a stimulating environment for a young researcher in theoretical physics. In the early 1930s, the Berkeley Radiation Laboratory of the University of California had hosted the first cyclotron ever built, following the ideas of Ernest O. Lawrence. In the 1960s, the recently renamed Lawrence Berkeley National Laboratory was still one of the major facilities in high-energy physics thanks to the powerful cyclotrons and synchrotrons that were being employed and developed there. Beside this laboratory, a strong theoretical group had been collaborating with the experimental teams in the interpretation of the data on the novel particles that had been discovered from the late 1940s onward.

When Gross began his PhD at Berkeley, Chew was the leader of the theoretical group. Starting from the late 1950s, Chew had been pursuing a programme aimed at interpreting the strong interacting particles without any reference to the quantum field theoretical framework. Chew’s programme was known as the ‘S-matrix bootstrap theory’ and had gained momentum within the community of theoretical physicists because it promised to overcome some of the major difficulties related to the quantum field theoretic approach to strong interactions. Graduate students and postdocs working at Berkeley all were contributing to this project, and Gross was no exception. Gross learned to appreciate Chew’s promising approach, and wrote his dissertation on multi-body N/D equations employing the formalism elaborated by Chew.

From bootstrap theory to quantum field theory

According to the recollections of various theoretical physicists, quantum field theory had fallen in disgrace in the mid-1950s. The success of the renormalization theory for relativistic quantum electrodynamics (QED) elaborated principally by S.-I. Tomonaga, J. Schwinger, R. Feynman—who were jointly awarded the 1965 Nobel Prize in Physics—and F. Dyson in the 1940s had given hope that this approach could be extended to both weak and strong interactions. In the 1950s, however, it became clear that the extension of renormalization theory to other interactions was far from straightforward. As for the strong interaction, the major problem was that the large coupling constant made the perturbation theory useless. Since the renormalization procedures were understood as a means to calculate the observable effects of the interactions between fields, where these interactions could be considered as small perturbations of a non-interacting theory of free fields, the application of renormalization techniques to strong interactions seemed meaningless.

Moreover, around 1959 the prominent Soviet physicist Lev D. Landau had declared that quantum field theory was “dead,” because of what came to be known as the ‘zero-charge problem.’ Landau and his collaborators had studied the behaviour of QED at high energies. By exploring the relationship between the charge appearing in the Lagrangian before renormalization—the ‘bare’ charge—and the observed charge, the Soviet scholars found that in the ultra-violet region the observed charge became zero whatever the value of the ‘bare’ charge. This result signalled a deep inconsistency of QED. Since this theory was considered the quantum field theory *par excellence *—the model on which further elaborations had to be based on—Landau assumed that the ‘zero-charge problem’ made inconsistent the concept of local quantum field theory altogether.

One of the main escapes from this unfavourable situation was to proceed in extrapolating phenomenological rules that reproduced experimental results, while ignoring the underlying micro-dynamics. In the late 1950s, a set of rules and procedures was established, which allowed theoreticians to get along without any reference to the quantum field theory, although several of the employed equations were actually derived from quantum field theory and perturbation theory. Chew championed one of the most radical versions of this phenomenological approach to strong interaction, based on using the observed dispersion relations in particle scattering to formulate a consistent S-matrix for infinitely many types of particles. This approach allowed for an immediate comparison with experiments, without dealing with conceptual problems concerning the consistency of the perturbation theory. Due to this malleability, Chew’s bootstrap theory became popular among theoretical physicists who were eager to find useful calculation tools for establishing a relation with experimental outcomes.

As many other students of Chew’s, Gross was captured by the bootstrap approach and began his original research by applying this method to various problems. After his graduation, however, Gross changed his mind and began to explore alternative methods. Gross’s conversion depended on several different inputs that added up to give him a different understanding of particle interactions.

**Quarks and the Scaling of Lepton-Hadron Scattering **

At the time Chew was developing and promoting his theory, M. Gell-Mann and, independently, G. Zweig proposed that hadrons could be made out of fractionally charged constituents called quarks. Both Gell-Mann and Zweig had arrived at this bold idea by analysing the symmetry structure of strong interacting particles. However, the quark hypothesis was understood mainly as a mnemonic mathematical device that helped in classifying the hadrons. Chew strongly opposed this view by hypothesising that there was no hierarchy among particles. Chew explicitly talked of “nuclear democracy” to emphasise that there was no clear cut distinction between elementary particles, composite particles, and force carriers. Each particle was a composite of the others. As a consequence, an acceptable theory, Chew stressed, should treat all the particles on the same footing.

Gross began to distance himself from Chew’s school in 1966 for conceptual reasons. Impressed by some methodological remarks by F. Low—one of the earlier proponents of the S-matrix theory—Gross recognised that the bootstrap theory lacked strong predictive power. While he was looking for more powerful dynamical schemes, Gross became impressed by the results of the sum rules derived by current algebra, and immediately began making research in this field. Gross’s new professional experiences also had a role in shaping his approach to theoretical particle physics. Soon after having earned his PhD, Gross became a Fellow of the Harvard Society and, in 1969, joined Princeton University as a faculty member, where he would stay for about thirty years. Both these institutional settings promoted a view of strong interactions rather different from the one that was cultivated at Berkeley. In collaboration with theoretical physicists working at Harvard (including S. Coleman, R. Jackiw, and C. Callan) Gross explored the Sugawara model—a theory of local currents in which the energy-momentum tensor was expressed as a product of currents. Among the various works carried out by Gross, the Gross-Callan sum rule, developed in 1958 to put the Sugawara model to test, had particular relevance.

In September 1968, J. D. Bjorken put forward that the Callan-Gross sum rule suggested the scaling behaviour in the deep inelastic scattering cross sections of lepton-nucleon collisions. The Bjorken scaling—as it came to be called—predicted that hadrons behave as collections of point-like particles. This prediction was employed to analyse the results of lepton-nucleon scatterings that were under investigation at the SLAC. This analysis seemed to confirm that hadrons were indeed built of point-like free particles. Further theoretical scrutiny led Gross and others to derive that these point-like particles had the same quantum numbers as Gell-Mann’s quarks. As Gross later recalled, after these experiments he “was then totally convinced of the reality of quarks.”

**The Gross-Wilczek Collaboration and the Discovery of Asymptotic Freedom**

By 1970, Gross had defined a clear target of his research programme: to explain the experimental scaling starting from the quark picture. There was a seemingly insurmountable anomaly in the scaling phenomenon of strong interactions. While at high energy (and short distance) quarks seemed to behave as free particles, nobody had ever observed such fractionally charged elements, as if they were permanently confined into the hadrons. The contradiction between an extremely strong attraction and quasi-free behaviour at short distance seemed to be irreconcilable.

Gross was led towards the research on asymptotic freedom of non-Abelian gauge theories—the Yang-Mills fields—because of the incongruence between the scaling behaviour and the field theoretic approach to quarks. In the early 1970s, new theoretical tools had been developed and employed for the analysis of high-energy interactions. Particularly influential was the renormalization group that in those years was being employed by several physicists, notably K. Wilson. Renormalization group techniques allowed for a study of the behaviour of the renormalized coupling constant as a function of the energy scale. Applications of the renormalization group in quantum field theoretic context had convinced Gross that only a free non-interacting theory could produce exact scaling, in open contradiction with the deep inelastic scattering observations. On the other hand, the recent proof provided by ‘t Hooft in 1971 that massive Yang-Mills fields were renormalizable had completely changed the perspectives of physicists concerning the consistency of the quantum field theoretical treatment of particle physics. After ‘t Hooft had made his momentous discovery, Yang-Mills fields became a central object of study because they were considered a reliable framework for the realistic description of particle behaviours. One of the main outcomes of this change of perspective was the growth of experimental research on the Glashow-Weinberg-Salam theory, which was being considered a good candidate for the unification of weak and electromagnetic interactions.

In this complex context started the work that led to the discovery of asymptotic freedom as well as to the emergence of quantum chromodynamics. The recent developments implied that the Yang-Mills quantum field theory could explain also strong interactions. In addition, renormalization group techniques provided the means for studying the behaviour of these kinds of theories at short distance. By the end of 1972, Gross had already acquired a good familiarity with such techniques and could precisely formulate the problem: he wanted to demonstrate that local field theory could *not *be the right theory for strong interaction by showing that such a theory was irreconcilable with the experimental fact of scaling. In order to demonstrate that this was the case, he envisioned a two-step plan. The first part was to show that only asymptotically free theories could explain scaling. Second, he wanted to demonstrate that local field theories were not asymptotically free. By applying renormalization group procedures, Gross and Callan demonstrated that in order to have a scaling behaviour the field had to be asymptotically free. They were able to show that this was true for all field theories except non-Abelian gauge theories. Gross, then, proceeded to demonstrate that no renormalizable quantum field theory was asymptotically free. Again, his demonstration did not include non-Abelian theories. To enlarge his demonstration to this set of theories he began collaborating with a PhD student of his who had recently switched his field of study from mathematics to theoretical physics: Frank Wilczek.

Since his early days as professor of physics, Gross developed a teaching methodology that entailed a strong collaboration with his graduate students on the topics he himself was investigating. This teaching practice proved to be very productive in the discovery of asymptotic freedom. In the autumn of 1972, Gross and Wilczek joined forces to calculate the beta-function describing the dependence of the coupling constant from the energy scale for the Yang-Mills theory, with the conviction that this computation would demonstrate that Yang-Mills fields were not asymptotically free. This computation required a deep clarification of the right techniques to employ in order to maintain gauge invariance. Gross and Wilczek completed this calculation by February 1973 demonstrating the contrary of what Gross had envisioned: Yang-Mills theory did present the property of asymptotic freedom and, as a consequence, could be a good candidate for the description of strong interaction. At the same time, a similar calculation was carried out by Hugh D. Politzer—then a PhD student at Harvard—who found an identical result. The two articles by Politzer and Gross & Wilczek appeared side by side in the journal Physical Reviews Letters in June 1973. Their work made it clear that a Yang-Mills theory of quarks was consistent with the scaling in deep inelastic scattering experiments. Moreover, the previous results obtained by Gross demonstrated that non-Abelian gauge fields were the only ones to possess the property of asymptotic freedom. Gross and Wilczek continued to investigate the asymptotic freedom of the Yang-Mills theory of strong interaction, and a few months later they published a long two-part paper entitled “Asymptotically free gauge theories,” which made clear the implications of their discovery. From 1973 onward, many theorists contributed to give a consistent shape to the Yang-Mills theory of quarks and gluons based on the SU(3) colour gauge symmetry structure, that is QCD. Although some problems persisted—such as the quark confinement problem—QCD was considered one of the best candidates for the description of strong interactions, and in a few years it came to be known, along with the Glashow-Weinberg-Salam electroweak theory, as the Standard Model of particle physics. “For the discovery of asymptotic freedom in the theory of the strong interaction," Gross was awarded the 2004 Nobel Prize in Physics jointly with Wilczek and Politzer.

**Beyond the Standard Model**

While the agreement between the theoretical predictions of the Standard Model of particle physics and high-energy observations has been excellent, theoretical physicists have been continuing to explore theoretical models that could provide a deeper understanding of nature as well as a unified picture of the four fundamental forces. The Standard Model has been successful in giving a unified description of electromagnetic, weak and strong interaction, but the extension of renormalized quantum field theory to gravity has been compromised by severe difficulties. Moreover, the work on dynamical problems of QCD in order to find analytic solutions to compare with experiments did not meet with success, even if some progress was made. In the early 1980s, Gross shifted his interest towards more “speculative physics,” as Gross called the research on quantum gravity and the unification of fundamental interactions in his Nobel Prize autobiographical sketch. He became one of the leading theorists working on string theory. String theory had been introduced in 1968 by the Italian physicist Gabriele Veneziano who had proposed an explanation of strong interactions in a theoretical framework derived from the bootstrap programme. Later, it was recognised that Veneziano’s proposal could be formulated by replacing point-like particles with one-dimensional objects, called strings. Various theoretical physicists developed the string theoretic programme, and in 1974 it was suggested that string theory could serve as a theory of gravity. However, the successes of QCD led the majority of physicists to dismiss the string theoretical approach, focusing instead on the elaboration of quantum field theories of particle interactions.

In the early 1980s, this situation changed thanks to what is usually called the ‘first superstring revolution,’ initially sparked by the work of the theoretical physicist Edward Witten—a former PhD student of Gross’s. Gross played a key role in this theoretical transformation. Along with Jeffrey A. Harvey, Emil Martinec, and Ryan Rohm, Gross developed the heterotic string theory in 1985, and for this endeavour they were jokingly called the “Princeton string quartet.” The heterotic string was a hybridization of two different approaches: superstring and bosonic string. The heterotic string theories served as major candidates for the string theoretical understanding of gravity before the so-called ‘second superstring revolution’ occurred in the mid-1990s, when it was understood that the five string theories developed until then might be included in a single and more general theory, christened M-theory. Apart from the heterotic string theory, Gross had continued to publish major works in the string theoretical framework and had trained a considerable number of first-rate theoretical physicists. Currently, he is member the Kavli Institute for Theoretical Physics in Santa Barbara, CA, where he continues to pursue his interest in high-energy physics, string theory and quantum field theory.

**Bibliography **

Gross, D. J. (2004) David J. Gross – Biographical. Nobelprize.org. Nobel Media AB 2013. Accessed 14 Mar 2014. http://www.nobelprize.org/nobel_prizes/physics/laureates/2004/gross-bio.html

Gross, D. J. (2005) The discovery of asymptotic freedom and the emergence of QCD. Proceedings of the National Academy of Sciences of the United States of America, 102(26), pp. 9099-9108.

Hoddeson, L., Brown, L. M., Riordan, M., & Dresden, M. (1995) The Rise of the Standard Model: Particle Physics in the 1960s and the 1970s. Cambridge University Press, Cambridge.

Kaiser, D. (2009) Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics. University of Chicago Press, Chicago.

Pais, A. (1986) Inward Bound: Of Matter and Forces in the Physical World. Clarendon Press, Oxford.

Pickering, A. (1999) Constructing quarks: A sociological history of particle physics. University of Chicago Press, Chicago.

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