Prof. Dr. Murray Gell-Mann > Research Profile
by Roberto Lalli
Nobel Prize in Physics 1969
"for his contributions and discoveries concerning the classification of elementary particles and their interactions".
Murray Gell-Mann is one of the physicists who have contributed most to the theoretical understanding of the interactions between elementary particles. Many of his papers are considered milestones in the rise of the Standard Model of particle physics. The evolution of Gell-Mann’s intellectual struggle to cope with particles’ behaviour well illustrates the tortuous path that led to the formulation of both quark-gluon chromodynamics and the unification of weak and electromagnetic interactions between the early 1950s and the mid-1970s. After World War II, the world of the practitioners of physics was very different from the one in which the previous generation of physicists used to work. Historians have coined the term Big Science to describe the deep transformations following the enormous growth of the scientific community and its involvement in large-scale projects. Although these radical social changes affected experimental activities more than theoretical endeavours, also theorists had to re-configure their role in a landscape made of a massive number of published papers as well as of an immense amount of data produced by new facilities, such as high-energy particle accelerators. In such a period of social changes and theoretical confusion, Gell-Mann played a leading role to put order in the families of particles that were continuously discovered. Starting from 1953, Gell-Mann made many proposals for studying the particle zoo and classifying its components. In the following years, physicists have recognized that several of these proposals were on the right track. Strangeness, quarks, colour, and chromodynamics, all these terms were born from Gell-Mann’s fertile imagination. While his main achievements ranged from the proposal of the “strange” quantum number to the development of the quantum field theory of quarks and gluons, the 1969 Nobel Prize in Physics was principally motivated by his classification of hadrons. Gell-Mann christened this classification the “eightfold way,” as an ironical reference to the Eightfold Path of Buddhism. The eightfold way organized the strongly interacting particles into groups containing elements having same spin and parity according to an underlying approximate symmetry, later called flavour symmetry. In the group-theoretical language, these groups of particles form irreducible representations of the special unitary group in three dimension SU(3). This step was essential in the theoretical developments that eventually led to formulation of quantum chromodynamics, which successfully explains several high-energy observations made in the last decades.
Becoming a Theoretical Physicist in the United States after World War II
Gell-Mann was born in New York City on the 15th of September 1929 to Jewish parents both emigrated from the Austrian part of the Austro-Hungarian Empire around the beginning of the 20th century. His father, Arthur Gell-Mann, was profoundly fascinated by physics, mathematics and astronomy. He tried to learn advanced topics, and showed an intense interest for Einstein’s general relativity. Thanks to the intellectual curiosity of his father, Gell-Mann benefited from an equipped library at home and got in touch with complex themes very early in his life. He was considered a child prodigy in several subjects, which gave him the possibility to build a scholarly career in different areas. After the end of the Grammar School - which Gell-Mann completed when he was just 14 – his father convinced Gell-Mann to pursue the study of physics because he would study the “beautiful” relativity and quantum mechanics. Although Gell-Mann favoured natural history and archaeology, he followed his father’s suggestion, applied for the Medill McCormick scholarship to study physics at the Yale University – and won. Gell-Mann tells that he was fascinated by relativity and quantum mechanics, just as his father had predicted.
At Yale he was captivated by the lectures of the physicist and philosopher of science Henry Margenau who taught physics paying strong attention to its foundations. After having earned his Bachelor’s degree in physics in 1948, Gell-Mann applied to different institutions in order to pursue his graduate studies and won a full scholarship from the Massachusetts Institute of Technology, where he worked under the supervision of Viktor “Viki” Weisskopf. The Austrian-born American theoretical physicist advised Gell-Mann not to focus only on fundamental questions, but to work on as many problems as possible in which he could learn how to successfully apply theoretical techniques. Gell-Mann later referred that this teaching was essential in the development of his style through which he reached the heart of a problem following more indirect routes. When Gell-Mann gained the PhD in 1951, the most common path for recent PhDs in theoretical physics was to spend a postdoctoral period at the Institute of Advanced Study in Princeton, then directed by J. Robert Oppenheimer. Gell-Mann stayed at the Institute one year. In this period, he developed insights in the application of novel theoretical tools - such as the Feynman diagrams - and directed his attention to the most problematic theoretical issues. Oppenheimer suggested him to focus on the theoretical explanation of the numerous particles that were being discovered. This suggestion found a perceptive listener. One year later, Gell-Mann was already developing views of particle interactions that, in ten years, would lead to a fruitful classification of hadrons and successful predictions of yet-to-be-discovered particles.
The Long March from Strangeness to the Eightfold Way
After his year in Princeton, Gell-Mann was offered a position as instructor at the University of Chicago. There, the Physics Department counted on several prestigious members as well as bright postdocs and graduate students. Gell-Mann began collaborating with Marvin “Murph” Goldberger on the quantum field theory of the pion-nucleon interaction. This research led Gell-Mann to the introduction of a new quantum number: strangeness. Starting in 1947, cosmic ray observations had been showing the existence of several heavy particles whose behaviour was difficult to explain. These particles where then called V-particles from the peculiar picture they formed in particle detectors. The most troubling feature of the V-particles was that they were produced copiously in particle collisions, but decayed very slowly. This behaviour seemed to indicate that the new particles were formed in strong interactions, but that they decayed according to the rules of weak interactions - a feature that many thought could be explained only by some kind of selection rule. In 1953, Gell-Mann began proposing that there was a new quantum number (later called strangeness). Gell-Mann assigned to the strongly interacting particles various values of the “strange” quantum numbers S, from -2 to 1. The particles that had S different from zero were later called “strange” particles. This number, Gell-Mann supposed, was conserved in strong interactions, while in weak interactions it was not. According to Gell-Mann’s hypothesis, and the simultaneous one put forward by K. Nishijima, the decay of strange particles through strong interactions was forbidden by this conservation principle, while strangeness could change only in weak interactions following some selection rules. Both Nishijima and Gell-Mann continued to develop the strangeness scheme and, around 1956, the strange quantum number began being broadly used within the physics community.
The phenomenological theory Gell-Mann and Nishijima ideated helped to solve several problems, including to relationship between the charge of mesons and baryons (namely, the hadrons) and three quantum numbers: isospin I, baryon quantum number B, and strangeness S. By 1960, though, the evolution of particle accelerators and detectors had led to the discovery of still more particles, including the so-called hadron resonances, which are short-lived excitations of pions, nucleons, and strange particles with well-defined masses and spins. These observations soon sparked many questions: Which was the difference between short-lived resonances and the group of already known strongly interacting particles formed by pions, nucleons, and strange particles? Were all these particles elementary? Or were some of them composite of others? Was it possible to find a deeper symmetry of strongly interacting particles that included isospin and hypercharge (then defined as the sum Y=B+S), and which could unify strange and non-strange particles?
Starting from 1960, Gell-Mann realized that the last question was the fundamental one and found a promising response. Simultaneously with, and independently from, Israeli theoretical physicist Yuval Ne’eman, Gell-Mann developed the view that strongly interacting particles might be classified by extending the isospin group SU(2) to an approximate SU(3) symmetry. Following this approach, Gell-Mann recognized that spin ½ nucleons N and hyperons (Λ, Σ, and Ξ) formed an octet representation of SU(3), and the same might hold for mesons (the three pions, the four K-mesons and a predicted particle of isospin I=0). In 1961, the predicted eighth pseudoscalar meson (called η meson) was found, and such a discovery was taken as a proof that the SU(3) scheme was an appropriate way to understand the behaviour of hadrons. In 1961 and 1962, Gell-Mann published the two papers “The Eightfold Way: A Theory of Strong Interaction Symmetry”, and “Symmetries of Baryons and Mesons”, which contain the theoretical framework for the classification of strongly interacting particles, including the “Gell-Mann matrices” of the infinitesimal generators of the group SU(3) and a formula that accounted for the difference of mass among baryons as well as among mesons. The latter formula was independently derived by S. Okubo in 1962, and is now called the Gell-Mann-Okubo mass relation formula.
After having noticed that experiments well satisfied the Gell-Mann–Okubo formula, Gell-Mann focused on the short–lived spin 3/2 hadron resonances. According to the SU(3) scheme, they should form a decuplet, but only nine of them had been actually observed by 1962. By employing the mass relation formula, Gell-Mann predicted the mass of this particle, in addition to the electrical charge and quantum numbers derived by the SU(3) representation. In 1964, the Ω-particle was observed at the Brookhaven National Laboratory. Many believe that this discovery was the main factor leading to the acceptance of the SU(3) symmetry and to the Nobel Prize awarded to Gell-Mann in 1969 “for his contributions and discoveries concerning the classification of elementary particles and their interactions.”
Quarks Enter the Scene
The same year of the discovery of the Ω-particle, Gell-Mann made another fundamental contribution to the classification of hadrons: Independently of his former student George Zweig, Gell-Mann proposed that strongly interacting particles might be formed of smaller fractionally charged particles. Taking seriously the SU(3) symmetry, one might wonder why the fundamental three-dimensional representation of the group is missing in nature, and one observes only octets and decuplets. This reasoning led Gell-Mann and Zweig to hypothesize that baryons might be constructed out of three constituents, and that mesons were composed of one of these particles plus its antiparticle. From James Joyce’s book Finnegans Wake, Gell-Mann borrowed the name “quarks”, and the name has endured ever since. Gell-Mann proposed the existence of three different quarks and anti-quarks: the up quark (u) with charge 2/3, the down quark (d) with charge -1/3, and the strange quark (s) with charge -1/3.
The three-quark hypothesis solved many problems, but had a great handicap: The quarks were fractionally charged and no such particle was ever observed. This feature led to several conceptual problems, and the status of these objects remained controversial. Many, including Gell-Mann, often used these particles only as mnemonic devices to classify particles without referring to any objective existence.
The situation completely changed at the end of the 1960s, when observations of the inelastic scattering of electrons on protons as well as of neutrinos on nucleons suggested that nucleons were made of point-like constituents. In a few months, these results gave a strong impulse to reconsider the quark model and several different theoretical approaches were developed to cope with these entities.
Towards a Quantum Field Theory of Fundamental Interactions
So far, I have summarized the work on the phenomenological rules Gell-Mann made in the period between the early 1950s to the late 1960s. In the same period, he also tried to understand these rules as a manifestation of an underlying dynamical theory. The search for a theoretical picture that could successfully explain the known fundamental interactions was an endeavour in which many theorists participated, and the historical construction of the Standard Model was far from straightforward. Gell-Mann contributed significantly to this collective effort by putting forward some ideas and methodologies (including the quark picture) that were later fully integrated in the quantum field theories of strong and electroweak interactions.
In 1954, along with his friend and collaborator Francis Low, Gell-Mann introduced a method, now called “renormalization group”, in which the coupling constant of quantum electrodynamics is studied as a function of the momentum transfer. In the following years, such a method played an important role in the development of quantum chromodynamics since it was employed to determine that the coupling strength between quarks and gluons tends asymptotically to zero as distance decreases (a feature called asymptotic freedom). In addition, Gell-Mann’s student Kenneth Wilson applied the method to phase transitions in condensed matter physics. “For his theory for critical phenomena in connection with phase transitions,” Wilson was awarded the 1982 Nobel Prize in Physics.
In 1956, following the discovery that parity was violated in weak interactions, Gell-Mann and R. Feynman developed the V-A theory of weak interactions, simultaneously proposed by Robert Marshak and George Sudarshan. The V-A theory describes all currents occurring in weak interactions as a composition of vector currents V and axial vector currents A. Developments of this theory in conjunction with some fundamental advances in the understanding of the Yang-Mills non-Abelian gauge invariant theory, eventually led to the electroweak unification, constructed principally by Sheldon Glashow, Abdus Salam, and Steven Weinberg between 1961 and 1968.
Gell-Mann’s most influential pursuits probably are on the formulation of the non-Abelian gauge theory of strong interactions. Apart from the achievements discussed in the previous sections, Gell-Mann made several contributions that made him one of the fathers of chromodynamics. Among them, there is the proposal that quarks had another quantum number: colour. Since the late 1960s, the views the nucleons and mesons might be complex system of more fundamental point-like particles had gained momentum. The quark model had a great problem, however. They were ½ spin particles and should obey Fermi-Dirac statistics. In some hadrons, such as the negatively charged Ω-particle formed by three strange quarks, the total wave function was symmetrical under the interchange of any two quarks. This was at odds with the Pauli exclusion principle. In 1971, Gell-Mann, with his colleagues William Bardeen and Harald Fritzsch, formalised a new symmetry group SU(3) based on the idea that quarks had an exactly conserved quantum number that could assume values from 1 to 3, and called this quantum number colour. They demonstrated that this hypothesis led to exact predictions about the weak interactions of hadrons, such as the pion decay. They also pointed out that a Yang-Mills gauge theory might be the right theoretical framework for the description of strong interactions. In 1973, David Politzer, and, independently, David Gross and Franck Wilczek demonstrated that such a gauge theory exhibited the property of asymptotic freedom. In the paper “Advantages of the Color Octet Gluon Picture, ” Gell-Mann, Fritzsch and H. Leutwigler soon reviewed the gauge invariant quantum field theory of coloured quarks and eight gauge bosons (called gluons). With this paper, chromodynamics was established as a leading candidate for the description of strong interactions.
A Return to Old Interests
The range of Gell-Mann’s intellectual achievements and interests go well beyond those summarized in the previous sections: He has contributed to the development of current algebra; for a certain period, he favoured the bootstrap theory that competed with the quark picture; and he was also fascinated by the string theory, which he supported with enthusiasm. Starting from the 1980s, Gell-Mann has somewhat come full circle. He turned to his childhood interest for different topics including historical linguistics, archaeology, and natural history. He has been bringing many of these topics together by furthering the study of complex adaptive systems. Gell-Mann is pursuing his researches on complexity as Distinguished Professor of the Santa Fe Institute, which he funded with other scholars in 1984. In 1994, Gell-Mann has popularized his personal views on the relationship between physics and philosophy as well as between elementary and complex systems in the book The Quark and the Jaguar: Adventures in the Simple and the Complex. Apart from his attention to and knowledge of different disciplines, the book also shows Gell-Mann’s strong attention towards environmental problems, which has been worrying Gell-Mann since his youth.
Brockman J. (2003) The Making of a Physicist: A Talk with Murray Gell-Mann. Available at http://www.edge.org/conversation/the-making-of-a-physicist (retrieved December 1 2013)
Brown, L. M., Dresden, M., & Hoddeson, L. (Eds.) (2009) Pions to Quarks: Particle Physics in the 1950s. Cambridge University Press, Cambridge.
Fitch V. L., & Rosner L. (1995) Elementary Particle Physics in the Second Half of the Twentieth Century. In Brown, L., Pippard, B., & Pais, A. (Eds.). Twentieth century physics (Vol. 2). AIP, New York, pp. 635-794.
Fritzsch H. (ed.) (2010) Murray Gell-Mann: Selected Papers. World Scientific, Singapore.
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.
Pais, A. (1986) Inward Bound Of Matter And Forces In The Physical World. Clarendon Press, Oxford.