# SCIENTIFIC WORK

Gürsey’s work in theories of elementary particles and general relativity is characterized by his skill in discovering symmetries in physical systems and his ability to express them mathematically through group theoretical methods, an approach pioneered by Hermann Weyl and Eugene Wigner in the 1930s. As specific examples, one may cite the nonlinear chiral sigma model, his proposal (with Luigi Radicati) for classifying hadrons into representations of the SU(6) algebra, the de Sitter and the conformal groups in relativity, and grand unified theories based on exceptional Lie groups.

**Youth and Education** . Feza Gürsey’s father, Reşit Gürsey, was a military doctor of wide-ranging intellectual and scientific interests, in pursuit of which he traveled to Vienna in the 1920s to learn about quantum mechanics. His mother, Remziye Hisar, received a PhD in chemistry at the Sorbonne in the same decade, when it was highly unusual for European women to do so, let alone women from more traditionally conservative societies. The parents had met in post–World War I revolution- and war-torn Baku, Azerbaijan, having independently arrived there from Istanbul. After receiving his primary education in Paris and secondary education at the elite Galatasaray Lycée in Istanbul, Feza Gürsey obtained his degree in physics-mathematics from the Science Faculty of Istanbul University in 1944. He worked briefly as an assistant at Istanbul University before receiving a Turkish Ministry of Education scholarship to do a PhD in physics at Imperial College, London. His 1950 study of the statistical mechanical analysis of a one-dimensional classical rectilinear assembly of interacting particles became relevant in the 1990s to the study of carbon nanotubes. He returned to Istanbul University as an assistant after spending 1950–1951 as a postdoctoral fellow at Cambridge University, England, and married Suha Pamir, also an assistant in the Istanbul University physics department, in 1952.

**Istanbul, Brookhaven, Princeton, and Columbia** . Between 1951 and 1956 in Istanbul, Gürsey published papers on the conformal group, quaternions, the classical spinning electron and the Dirac equation, and a conformally invariant version of Heisenberg’s nonlinear spinor theory. The conformal group includes scale transformations and inversions of spacetime coordinates in addition to the rotations and Lorentz transformations from one inertial frame to another that define the Lorentz group; it is relevant for physical systems without a built-in mass or length scale. These subjects were by no means mainstream research topics for the newly developing area of particle physics, which was at that time focused on identifying new unstable particles found in cosmic rays or accelerators and understanding their interactions. The significance of the conformal group was widely appreciated much later, first upon the observation of scale invariance in deep-inelastic electron or neutrino-nucleon scattering experiments in the 1970s, and then in the 1980s, when conformal symmetry was shown to be sufficient for a providing a complete solution of two dimensional field-theoretic problems. Gürsey, with his student Sophocles Orfanidis, also anticipated the latter results in a pioneering paper in 1973. John Wheeler once wrote, “Gürsey, as a largely self-educated physicist, has a most valuable independence of point of view and originality” (read by Yale Prof. Vernon Hugues at the Feza Gürsey memorial service, 20 May 1992). In the light of Gürsey’s later work, it appears that a good part of this self-education took place in the 1951–1956 Istanbul period.

In 1957, Gürsey caught the attention of Wolfgang Pauli by a paper suggesting that the SU(2) isospin symmetry of hadrons, the strongly interacting particles, might emerge from mixing half-integer spin particles with their antiparticles. Pauli had originally introduced such a mixing, which came to be called the Pauli-Gürsey transformation, while examining the theory of beta-decay proposed by Enrico Fermi. Pauli and Werner Heisenberg attempted to incorporate this mechanism of symmetry generation into Heisenberg’s theory of a fundamental spinor field with a non-linear self-interaction, but the idea proved unfruitful in that context. However, generalized currents capable of simultaneously creating or destroying a pair of spin-1/2 particles, which is an essential feature of Pauli-Gürsey symmetry, were seen to be inevitable in the context of grand unified theories of strong, weak and electromagnetic interactions introduced by Howard Georgi and Sheldon Glashow and by Jogesh Pati and Abdus Salam in 1974.

From 1957 to 1961, Gürsey worked at the Brookhaven National Laboratory, the Institute for Advanced Study, Princeton, and Columbia University, meeting and collaborating with J. Robert Oppenheimer, Eugene Wigner and Tsung Dao Lee. His 1959 nonlinear sigma model is based on a proton-neutron isospin SU(2) doublet interacting with pions, particles which were at the time believed to be the main carriers of the strong force. The nucleon doublet is initially massless, and can thus generate two independent SU(2) symmetries through left and right-handed currents. The pions and their interactions with the nucleons are brought in via a nonlinear representation of this SU(2)_{L} × SU(2)_{R}*chiral*, or handed symmetry. The nonlinear interaction gives masses to the nucleons, but keeps the pions massless as required by the observed (partial) conservation of the weak pseudovector current. The model, while never claiming to be a fundamental theory of hadrons, introduced several important ideas: the first explicit example of a spontaneously broken symmetry, and the attendant appearance of massless bosons perhaps being the most important. Shortly afterward it was realized by Yoichiro Nambu, Jeffrey Gold-stone, and others that massless bosons would always accompany spontaneous symmetry breakdown when a system randomly settles into one of its many possible lowest energy states.

**Middle East Technical University, Ankara** . In 1961, Gürsey left Columbia University to take up a professorship at the newly founded Middle East Technical University in Ankara, Turkey, where he worked until 1969, except for brief visits to the Institute for Advanced Study at Princeton, the Brookhaven National Laboratory, and Yale University. He initially returned to General Relativity, reformulating the theory so that an overall factor in the metric of the universe serves as a cosmological scalar field and gives rise to effects expected from Mach’s principle. The novel scalar-field energy-momentum tensor introduced by Gürsey in this work was rediscovered about a decade later in studies of scale invariance. His work on spin-1/2 particles in de Sitter space also dates from this period; de Sitter space has attracted general interest since 1981, first upon Alan Guth’s proposal of an rapidly inflating early universe scenario, and later with observations that the expansion of the universe is accelerating.

Gürsey’s best-known work from this period is his identification of hadronic SU(6) symmetry in a paper he wrote with Luigi Radicati while visiting the Brookhaven National Laboratory in 1964. The idea that all hadrons are made up of hypothetical u, d, and s quarks had been introduced earlier by Murray Gell-Mann and George Zweig. Gürsey and Radicati proposed to extend the resulting SU(3) symmetry to SU(6) by considering the spin up and down states of each quark as separate particles. The surprising ability of SU(6) to explain and correlate a large mass of data strengthened the view that quarks were real physical constituents of hadrons, and not just mathematically useful but fictitious constructs. The success of SU(6), however, pointed to deeper problems. For example, the three-quark wavefunction for a proton or neutron seemed to be in conflict with the sacrosanct Pauli exclusion principle. Furthermore, confining the quarks to the volume of a proton would be expected to give them relativistic energies, at which only the total angular momentum of a quark would be conserved, while its spin by itself would not be. However, attempts to formulate a relativistic generalization of SU(6) not only failed to improve agreement with experiments, but also were proven to be forbidden on seemingly unassailable theoretical grounds, a situation reminiscent of aerodynamics proofs that the bumblebee should not be able to fly. The justification for SU(6) came ten years later when the field theory of strong interactions between quarks was formulated. The theory that has since become commonly known as Quantum Chromodynamics, or QCD for short, solves the Pauli exclusion problem by introducing a new degree of freedom called *color* for each quark. It also has the feature that the quark-quark interaction weakens as quarks get closer, explaining the separate conservation of spin and the success of SU(6).

**Yale University** . In 1969 Gürsey took up a professorship at Yale, filling the position of Gregory Breit who retired. He was appointed to the J. Willard Gibbs chair in 1977, holding the position until his own retirement in 1991. In this period, while continuing to work on non-linear chiral models, conformal symmetry and general relativity (in particular, on Kerr-Schild type metrics), he renewed his interest in quaternionic and octonionic structures, and suggested possible uses for them in physics. Pascual Jordan, John von Neumann, and Eugene Wigner, together with Abraham Albert, had already in the 1930s examined algebras of 3×3 real, complex, quaternionic and octonionic matrices subject to a non-commutative symmetric Jordan product. Their hope was to find alternative formulations of quantum mechanics through such Jordan algebras. From 1973 onwards Gürsey drew attention to the close links between the Exceptional Lie groups (F_{4}, E_{6}, E_{7}, E_{8}) and Jordan algebras, and proposed models of Grand Unified Theories (GUTs) based on E_{6} and E_{7}. In the following three decades, evidence accumulated that if some version of superstring/M-Theory succeeds as a quantum theory of all known interactions, octonions and Exceptional groups will figure prominently in it. From the phenomenological point of view, the most promising GUT groups are SU(5), SO(10) and E_{6}, where the first two may be also regarded as the exceptional groups E_{4} and E_{5}. One version of string theory, which aims also to include gravitation, naturally leads to the gauge group E_{8} × E_{8}. The E-series also appears in the reduction of eleven dimensional supergravity to lower dimensions. Among the many other suggestive connections between octonions and eleven dimensional superstring/M-Theory, one may mention that seven dimensions have to be compactified into a manifold of G_{2} holonomy in the reduction to four space-time dimensions. The smallest exceptional group G_{2} happens to be the automorphism group of octonion multiplications.

Feza Gürsey was given the Science Award of the Scientific and Technological Research Council of Turkey (TUBITAK) in 1969, the J. R. Oppenheimer Prize (with Sheldon Glashow) and the A. Cressey Morrison Prize (with Robert Griffiths) in Natural Sciences in 1977, the Albert Einstein Award in 1979, the College de France Award in 1981, the title of Commendatore by the Italian government in 1984, and the Wigner Medal of the Group Theory and Fundamental Physics Foundation in 1986. The Wigner Medal has been awarded biennially since 1977 at the International Colloquium on Group Theoretical Methods in Physics, a conference series Gürsey himself started in 1962 in Istanbul. He died in New Haven, Connecticut, on 13 April 1992. In recognition of his leading role in starting a school of theoretical physics in Turkey through the students he trained, TUBITAK, jointly with Bogaziçi University, established the Feza Gürsey Institute for research in theoretical physics and mathematics in 1996.

## BIBLIOGRAPHY

### WORKS BY GÜRSEY

“Classical Statistical Mechanics of a Rectilinear Assembly.” *Proceedings of the Cambridge Philosophical Society* 46 (1950): 182–194.

“On the Symmetries of Strong and Weak Interactions.” *Nuovo Cimento* 16 (1960): 230–240.

“Reformulation of General Relativity in Accordance with Mach’s Principle.”*Annals of Physics* 24 (1963): 211–242.

“Introduction to Group Theory.” In *Relativity, Groups and Topology*, edited by C. DeWitt and Bryce DeWitt. New York: Gordon and Breach, 1964. Lectures delivered at Les Houches during the 1963 session of the Summer School of Theoretical Physics, University of Grenoble.

“Introduction to the de Sitter Group.” In *Group Theoretical Concepts and Methods in Elementary Particle Physics; Lectures*, edited by Feza Gürsey. New York: Gordon and Breach, 1964. Proceedings of the Istanbul Summer School of 1962.

With Luigi Radicati. “Spin and Unitary Spin Independence of Strong Interactions.” *Physics Review Letters* 13 (1964): 299–301.

With Sophocles Orfanidis. “Conformal Invariance and Field Theory in Two Dimensions.” *Physics Review* D7 (1973): 2414–2437.

With Pierre Ramond and Pierre Sikivie. “A Universal Gauge Theory Model Based on E_{6}.” *Physics Letters* 60B (1976): 177–180.

With Hsiung Chia Tze. “Complex and Quaternionic Analyticity in Chiral and Gauge Theories I.” *Annals of Physics* (1980): 128: 29–130.

With Yoram Alhassid and Francesco Iachello. “Group Theory Approach to Scattering.” *Annals of Physics* 148 (1983): 346–380.

With B. S. Balakrishna and Kameshwar Wali. “Noncommutative Geometry and Higgs Mechanism in the Standard Model.” *Physics Letters* B254 (1991) 430–434.

With Chia-Hsiung Tze. *On the Role of Division, Jordan and Related Algebras in Particle Physics*. Singapore: World Scientific, 1996.

### OTHER SOURCE

Bars, Itzhak, Alan Chodos, and Chia-Hsiung Tze, eds. *Symmetries in Particle Physics*. New York and London: Plenum Press, 1984.

*Cihan Saclioglu*