Research Profile

*by Roberto Lalli*

**Frank Wilczek**

**Nobel Prize in Physics 2004 together with David J. Gross and H. David Politzer**

**"for the discovery of asymptotic freedom in the theory of the strong interaction".**

Frank Wilczek is an American mathematician and theoretical physicist. During his PhD, when he was only 21 years old, Wilczek contributed to the discovery that a class of quantum field theories had the property of asymptotic freedom, i.e., has a coupling constant that tends asymptotically to zero when energy (distance) increases (decreases). This discovery was an essential step in the emergence and acceptance of the quantum field theory of strong interactions called Quantum Chromodynamics (QCD). In 2004, this discovery gained him the Nobel Prize in Physics jointly with his PhD supervisor David Gross and Hugh D. Politzer, who independently made the same discovery. Since 1973—the year of the discovery of the asymptotic freedom—Wilczek has been conducting important research on a large variety of topics, including the unification of the coupling constants in quantum field theory, the extension of quantum field theory techniques to condensed matter physics and cosmology, the behaviour of matter at ultra-high temperature and/or density, new forms of quantum statistics, and the quantum theory of black holes. Recognising the importance of communicating the meaning of his scientific activity, Wilczek has been actively involved in the popularisation of theoretical physics through articles and books for a lay audience as well as in training a large number of doctoral students.

From mathematics to theoretical particle physics

Frank Wilczek was born in Mineola, NY, on 15 May 1951 to parents whose families had emigrated from Europe after World War I. His father—the radio-TV repairman Franciszek Wilczek—was of Polish origin, while his mother’s parents came from Naples, Italy. Wilczek grew up in Queens, where he attended public schools with “excellent teachers,” as Wilczek maintains in his Nobel Prize autobiographical sketch. After graduating from Martin van Buren High School, Wilczek enrolled at the University of Chicago wishing to become a scientist. Since he was undecided about his field of specialisation, Wilczek chose to major in mathematics, which would provide a solid basis whatever his decisions would be. In Chicago, he was inspired by the lectures on the use of symmetry and group theory given by the Romanian theoretical physicist Peter Freund. Attending these lectures was Wilczek’s first serious contact with mathematical physics. They would have a long-lasting influence on Wilczek’s future choices.

After obtaining his bachelor’s degree in 1970, Wilczek pursued graduate studies at Princeton University receiving his Master of Arts in Mathematics in 1972. While his main field of study remained mathematics, his interest in physics was flourishing. Before receiving his M.A., Wilczek had taken the course on field theory given by the young Professor of Theoretical Physics David Gross. This course was so inspiring that Wilczek decided to switch from mathematics to theoretical particle physics pursuing his PhD studies under Gross’s supervision.

Gross employed a teaching methodology that entailed a strong involvement of students in the research Gross himself was pursuing. Sometimes, this involvement became a real and fruitful collaboration, as in the case of Wilczek. In the autumn of 1972, Gross and Wilczek began working together on a research project Gross was developing since 1970: the investigation of the relationship between quantum field theory and the experimental phenomenon of scaling. Between 1967 and 1968, experiments performed at the recently built Stanford Linear Accelerator on electron-nucleon collisions had shown a “scale invariant” distribution, independent of the energy of the incoming electrons—a behaviour that was called ‘Bjorken scaling’ after James Bjorken, who first provided a theoretical framework for the analysis of these surprising data. Bjorken scaling suggested that nucleons were composed of point-like particles that were called partons, following the theoretical model Feynman put forward in 1969.

These experimental results and a series of further theoretical investigations had convinced Gross that quarks were actual constituents of matter, and not simple mathematical devices, as they had been considered up to then. Around 1970, Gross began focusing on the understanding of the scaling phenomenon assuming that quarks were real. In 1971, a momentous discovery substantially changed theoretical physicists’ approach to the field theories of particle interactions. The Dutch theoretical physicist G. ‘t Hooft demonstrated that both massless and massive non-Abelian gauge theories—called Yang-Mills fields from the name of the two physicists who first put forward such theories—were renormalizable. ‘t Hooft’s work had a strong impact on the community of theoretical physicists because it showed that Yang-Mills fields might be suitable as the realistic description of particle interactions. An immediate outcome of this change was the revival of the Glashow-Weinberg-Salam theory of electroweak interactions, which became a principal area of investigation in both theoretical and experimental physics.

Moreover, useful theoretical tools for the study of quantum field theory were becoming familiar to a group of theoretical physicists. Gross and others were interested in the relationship between the quantum field theory of strong interaction and the scaling phenomenon. In order to pursue this project, it was necessary to investigate the variation of the coupling constant as a function of the distance. To this purpose, Gross could employ a formidable mathematical apparatus that had been recently rediscovered and applied successfully to condensed matter physics by K. Wilson and others: the renormalization group.

The renormalization group allowed for a study of the changes of a physical system in dependence of the energy scales. In 1970, the theoretical physicists C. Callan and K. Symanzik had extended the renormalization group approach to perturbation theory devising the ‘renormalization group equation,’ which allowed for the study of the dependence of quantum field theoretical predictions on momentum (or energy) scales. This study was realised by means of the analysis of the transformation of the effective coupling constant g described by the beta function

*β*

(

*g*

). Through the application of the renormalization group equation, Gross became convinced that only a free non-interacting theory could produce exact scaling. Following this belief, Gross envisioned a two-step project aimed at demonstrating that no local quantum field theory was in accord with the experimental fact of scaling. The first step was to prove that only those theories that possessed the property of asymptotic freedom agreed with scaling. Second, he wanted to demonstrate that

*no*

quantum field theory was asymptotically free.

**The Gross-Wilczek Collaboration**

By the time Wilczek began working with Gross, the first part of Gross’s project had been fulfilled. In addition, Gross had already worked out a convincing demonstration that all quantum field theories except for Yang-Mills fields were not asymptotically free. Thus, Wilczek and Gross focused on what they believed to be the final step of Gross’s original project: to provide a convincing demonstration that Yang-Mills theories were not asymptotically free, through the calculation of the beta function of the renormalization group equation.

To calculate this function, Gross and Wilczek had to deal with several issues such as the choice of regularization and gauge. One of the criteria that guided them was that the final result should be gauge invariant. This constraint proved to be very useful because it allowed for a check of the long and complicated calculations. By February 1973, they were completing the computation of the beta function, obtaining a result that seemed to show that the Yang-Mills fields were not asymptotically free, as Gross had envisaged. Wilczek and Gross, however, discovered that they had made a mistake resulting in the wrong sign of the final equation. The correct result came to them as a surprise because it proved the contrary of what they had expected. Before publishing the unforeseen discovery, Gross and Wilczek compared their result with that obtained by Harvard PhD student Politzer who was doing the same calculation. The beta functions they had obtained were identical, and Gross & Wilczek as well as Politzer published their papers side by side in the July 1973 issue of Physical Review Letters.

In their ground-breaking paper “Ultraviolet Behavior of Non-Abelian Gauge Theories,” Gross and Wilczek related their discovery of the asymptotic freedom of Yang-Mills fields to the suggestion that the Bjorken scaling might be obtained by a strong-interaction dynamics based on a Yang-Mills theory. A few months later, Gross and Wilczek published a long two-part paper entitled “Asymptotically free gauge theories,” in which they addressed in greater detail the implications of their discovery. The connection with the phenomenon of scaling was more clearly drawn through the calculation of the logarithmic deviation to scaling in the Yang-Mills fields. Moreover, it was explicitly proposed that the Yang-Mills theory of quark dynamics could be the right framework for the realistic description of strong interaction. Gross and Wilczek also analysed the various issues concerning the construction of this realistic model and proposed that the strong interaction was mediated by colour gauge groups. After addressing the problems of including spontaneous symmetry breaking, they also suggested that the symmetry might be exact. In this context, Gross and Wilczek explicitly referred to the unbroken SU(3) colour gauge group of quarks and gluons that had been suggested in the 1960s by Nambu and others, and recently advocated by Gell-Mann and his collaborators.

In the following years, the unbroken SU(3) non-Abelian gauge symmetry of quarks and gluons emerged as the most probable theory for a realistic description of strong interactions, and, by the late 1970s, it became widely referred to as quantum chromodynamics (QCD). The discovery of asymptotic freedom played a fundamental role in the emergence of QCD and its rapid acceptance among the community of theoretical physicists, because asymptotic freedom provided both the explanation for the scaling phenomena and a mechanism for the quark and gluon confinement.

During the 1970s, the consensus on the validity of what came to be called the Standard Model of particle physics—which included QCD and the Glashow-Weinberg-Salam gauge theory of electroweak interactions—steadily grew. In 1979, Glashow, Weinberg and Salam were awarded the Nobel Prize in Physics “for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current”—an event that indicated the broad acceptance of the this theory. While the experimental success of the SU(2)xU(1) gauge theory of electroweak interactions increased physicists’ confidence also in the validity of QCD, the tests of QCD proved to be much more problematic than those of the electroweak theory. The permanent confinement of quarks and gluons implied that such particles could be detected only through indirect means. In any case, various theoretical predictions of QCD—including the jet cross section, the scaling violation in deep inelasting scattering of lepton-hadron collisions, and the running of the coupling constant—have been in close agreement with a number of experiments performed from the mid-1970s onward. Since the late 1970s, the confidence in the validity of QCD has been growing, and, in 2004, Wilczek’s contribution to QCD was rewarded with the Nobel Prize in Physics “for the discovery of asymptotic freedom in the theory of the strong interaction“ jointly with Gross and Politzer.

**A Bridge Across Disciplinary Boundaries**

In his autobiographical sketch, Wilczek emphasises that “the unity of knowledge is a living ideal and goal.” With his own work, Wilczek has been trying to achieve this goal in many different ways. Since his early entrance to the scholarly world, he devoted his training as mathematician to the resolution of pressing physical problems. Later, he explored the connections between ‘fundamental’ and ‘applied’ physics. In his more than 40 years of research on the unity of knowledge, Wilczek has been producing a number of theoretical studies that are at the forefront of current research.

In the late 1970s, he proposed a model for solving the strong CP problem in QCD. His model—later known as the Weinberg-Wilczek model because it was simultaneously put forward by Weinberg—was based on the existence of hypothetical particles called axions. Wilczek studied the properties of these particles suggesting that they are possible constituents of cold dark matter. Although the Weinberg-Wilczek model is not considered as a realistic model any longer, the research on these hypothetical particles as components of dark matter is still very much alive.

Moreover, Wilczek made contributions to the exploration of new forms of quantum statistics. In the early 1980s, Wilczek studied the quasi-particles occurring in two-dimensional systems, which he baptised ‘anyons’ because they are neither bosons nor fermions. In 1985, in collaboration with Don Arovas and Bob Schrieffer, Wilczek demonstrated that the fractional quantum Hall effect requires particles with a statistics different from both bosons and fermions. In his efforts to connect the worlds of fundamental and applied physics, Wilczek has recently shown that not only is the theory of anyons interesting from a theoretical perspective, but that it also might lead to high-performance quantum computers. Currently, several research groups are devising experimental set ups aimed at detecting the existence of anyons.

At the end of the 1990s, Wilczek played a pivotal role in the revitalization of the research on colour superconductivity—a phenomenon analogous to electromagnetic superconductivity, which QCD predicts for quark matter at high density and relatively low temperature. Although previous studies had already discussed the phenomenon, Wilczek and his group at the Institute of the Advanced Study demonstrated that the phenomenon is much more relevant than originally assumed. This work, and a parallel one put forward by a theoretical group at Stony Brook University, sparked the interest in this phenomenon, and nowadays several physicists are working on the analysis of phase diagrams for dense quark matter.

Apart from these and several other contributions to advanced theoretical physics and its possible applications, Wilczek has dedicated much energy to the popularisation of the subjects to which he has been dedicating his life. He wrote several articles for journals such as Physics Today and Nature as well as four non-technical books, one of them together with his wife—the American journalist Betsy Devine. In his latest book for a lay audience—the

*Lightness of Being*

—Wilczek explores the modification of fundamental concepts related to the contemporary advancement of physics and shows how the old clear-cut separation between matter and light has been transcended in modern physics. Wilczek is currently Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology, where he continues his trip towards the theoretical understanding of nature and the unification of forces.

**Bibliography**

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.

Politzer, D. (2005) Nobel Lecture: The dilemma of attribution. Reviews of Modern Physics, 77(3), pp. 851-856.

Wilczek F. (2005)Frank Wilczek-Biographical. Nobelprize.org. Nobel Media AB 2013. Accessed 21 Mar 2014. http://www.nobelprize.org/nobel_prizes/physics/laureates/2004/wilczek-bio.html

Wilczek, F. (2005) Nobel Lecture: Asymptotic freedom: From paradox to paradigm. Reviews of Modern Physics, 77(3), pp. 857-870.

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