# Lochlainn O'Raifeartaigh

### Born: 11 March 1933 in Clontarf, Dublin, Ireland

Died: 18 November 2000 in Dublin, Ireland

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**Lochlainn O'Raifeartaigh**'s parents were Tarlach O'Raifeartaigh (1905-1984) and Neans Morrissey, known as Terry and Nancy Rafferty. Tarlach O'Raifeartaigh studied at University College, Dublin and was a Gaelic scholar who became Professor of History at St Patrick's Training College, Drumcondra, Dublin. Later he became Chairman of the Higher Education Authority and was Secretary to the Department of Education of Ireland.

**Lochlainn's mother, Neans, was the daughter of T J Morrissey. She studied mathematics at University College, Dublin, and was awarded a First Class degree. She became the Assistant Secretary at the Department of Education. A very talented person, she spoke English, Irish, French, German and Swedish, was a Japanese scholar, and had a passion for music. Lochlainn, born on Kincora Road, Clontarf, Dublin, was the second eldest of his parents' six children, having an older sister, two younger brothers and two younger sisters.**

O'Raifeartaigh's primary school education was at St Joseph's school, run by the Christian Brothers, in the Marino district of Dublin. He then studied at St Vincent's Castleknock College, a school set up in the 1830s in the Castleknock area of Dublin near Phoenix Park, designed to educate boys for the Catholic priesthood as well those aiming at a secular life. The College had 254 pupils in 1950 when O'Raifeartaigh graduated. His school record was outstanding and he was ranked first in Mathematics in the Irish Leaving Certificate Examination. He was awarded a University Entrance Scholarship to study at University College, Dublin. His original intention had been to study engineering but he changed his mind before beginning his university studies, opting instead for a mathematical sciences degree. Before matriculating at University College, Dublin, he spent the summer of 1950 cycling to Rome with four of his fellow classmates from Castleknock College. He studied mathematical sciences for his first degree, attended lectures by Erwin Schrödinger, and graduated in 1954 with a B.Sc. with First Class Honours. He continued to study at University College, Dublin, and was awarded a M.Sc. (1st Class) in 1956. Schrödinger retired in 1956 and left Ireland to return to Austria so O'Raifeartaigh went to the Dublin Institute for Advanced Studies where he worked under John Synge who held the post of Senior Professor in the School of Theoretical Physics of the Dublin Institute for Advanced Studies.

In addition to his studies of mathematics and physics at University College, Dublin, O'Raifeartaigh was also passionate about the Irish language. As an undergraduate he had joined An Cumann Gaelach (the Gaelic Society) which held a yearly meeting in an Irish speaking region of Ireland. This Society, which was open to all students in Irish universities, both north and south, held a meeting in Teelin near Donegal which was attended by O'Raifeartaigh and Treasa Donnelly. Treasa was a student at Queen's University Belfast who was also passionately interested in the Irish language. In addition, she was a student of Celtic Studies in Belfast who shared O'Raifeartaigh's love of the theatre and of hill walking. They married in 1958 and had five children, three sons and two daughters: Conor, Finbar, Cormac, Una, and Aoife.

O'Raifeartaigh began to undertake research towards his doctorate at the Dublin Institute for Advanced Studies in 1956, working under John Synge. In the following year, 1957, he was awarded a scholarship by the Dublin Institute for Advanced Studies which allowed him to continue his research abroad working with Walter Heitler (1904-1981) at the University of Zürich. Heitler, a leading expert on quantum theory, was a German Jew who had been forced to leave Germany in 1933. He had been at the University of Bristol for eight years before Schrödinger had arranged for him to go to Dublin and take up a professorship at the Institute for Advanced Studies. He had left Dublin in 1949 to take up a professorship at the University of Zürich. O'Raifeartaigh undertook research at Zürich, advised by Heitler, and was awarded a doctorate in 1960 for his thesis

*Non Local Field Theories*. Edmond Arnous had undertaken research in Paris working under Louis de Broglie and had then undertaken postdoctoral work with Heitler in Zürich. Heitler and Arnous had studied nonlocal field theories and, in his doctoral thesis, O'Raifeartaigh continued their work studying the

*S*-matrix in their nonlocal field theory. He was happy in Zürich and his first child Conor was born in 1960, the year he was awarded his doctorate. After obtaining his doctorate, O'Raifeartaigh returned to Dublin where he was appointed as an assistant professor of physics at the Dublin Institute for Advanced Studies in 1961. In the same year his second child Finbar was born.

Not long after taking up this appointment, O'Raifeartaigh was on a visit to Bern, Switzerland, when he met by chance the Indian theoretical physicist Ennackal Chandy George Sudarshan. This led to O'Raifeartaigh being invited to lecture at the Mathematical Science Institute in Madras, (now Chennai) India, which was just in the process of being founded in 1962. This Institute promoted fundamental research in theoretical computer science, mathematics, and theoretical physics. O'Raifeartaigh spent three months over the winter of 1963-64 at the Mathematical Science Institute in Madras where he lectured on local Lie groups and their representations. Returning to Dublin in the spring of 1964, he was awarded extended study leave which allowed him to make a lengthy research visit to Syracuse University in the United States. He had been invited to join Sudarshan's research group at Syracuse and he was delighted to be able to take advantage of the opportunity. Travelling to the United States with his family, he spent three years at Syracuse [5]:-

Writing about O'Raifeartaigh's Theorem, his son Cormac writes:-At Syracuse, O'Raifeartaigh made a discovery that established his reputation: He proved, in1965, that it was impossible to combine internal and geometric(relativistic)symmetries of the Lie group type in a nontrivial way. This result, which became known as O'Raifeartaigh's Theorem, brought to an abrupt end major efforts to effect this combination. Brilliant application of group theoretical methods, as manifested in this work, became a unifying theme in his long and distinguished career.

Remaining in the United States, O'Raifeartaigh spent the academic years 1967-68 at the Institute for Advanced Study at Princeton. He was offered a permanent position at Syracuse University but he now received an offer of a senior professorship at Dublin Institute for Advanced Studies. O'Raifeartaigh and his family had been very happy in Syracuse but they all felt that they should take the opportunity to return to Europe. In particular, they wanted to bring up their children in Ireland. He accepted the offer from Dublin where he would remain for the rest of his career. He did, however, spend some extended periods abroad. For example, he spent 1975-76 at the Institut des Hautes Études Scientifiques at Bures-sur-Yyvette near Paris. The family lived in the Résidence de l'Ormaille, which housed visitors to the Institute, and the children attended local schools during this year. O'Raifeartaigh made a second visit to the Institut des Hautes Études Scientifiques in 1983-84. He also made a visit to the University of Notre Dame, Indiana, USA in 1994. He was also active in the theoretical physics community in Ireland. Denis O'Sullivan writes [6]:-... the first proof of the 'impossibility' of combining internal symmetries with the Poincaré symmetry of space-time was furnished by ... Lochlainn O'Raifeartaigh. The 'O'Raifeartaigh no-go theorem' was a hugely controversial result at the time and brought quite a few Ph.D. studies to an abrupt halt ... My understanding is that the debate was finally closed when Coleman and Mandula published a generalization of the theorem. Given the controversy, it seems a pity that the original theorem is never referred to now(although it is liberally cited in the Coleman-Mandula paper)... in other words Dad got all the flak but is now forgotten!

Theoretical physics developed rapidly from the 1970s onwards with many of the new ideas related to areas in which O'Raifeartaigh was a leading expert, namely in using group theoretical methods. He made many fundamental contributions to non-abelian gauge theories. Siddhartha Sen in [6] lists his main contributions under the headings: (i) The Effective Potential; (ii) Magnetic Monopoles; (iii) Toda Theory and W-Algebras; and (iv) Seiberg-Witten Theory. He published several important books, the first beingLochlainn was a great supporter of the Institute of Physics in Ireland. He attended our first meeting in Carrickmacross in1972and in later years was present at a number of IOP Spring weekends, both North and South, along with his wife Treasa. He kindly accepted an invitation to deliver a talk at our recent meeting in Newcastle, Co Down in1999. Indeed he had a great ability to explain difficult concepts of high-energy physics to theorists and experimentalists alike. His contributions to the Royal Astronomical Society meeting in Dublin in1982, and at the opening ceremony of the221991^{nd}International Cosmic Ray Conference to a packed National Concert Hall in August, will be remembered for their excitement and clarity.

*Lectures on Local Lie Groups and Their Representations*(1964). After editing

*General Relativity; Papers in Honour of J L Synge*(1972), O'Raifeartaigh wrote a book on the topic for which he is most famous, namely

*Lecture Notes on Supersymmetry*(1975). He begins the introduction by writing:-

His next important book was the monographSupersymmetry is a new symmetry that has emerged in recent years. It has the property that it allows fields of different spin, and, in particular, boson and fermion fields, to appear in the same irreducible multiplet.

*Group Structure of Gauge Theories*in 1986. He writes in the Preface:-

He also wrote an important bookIt has been known for many years that the gravitational and electromagnetic interactions of matter can be formulated as gauge theories - based on the Lorentz group SO(3,1)and the compact 'internal' phase group U(1), respectively. But over the past two decades it has gradually come to be accepted that the remaining two(known)fundamental interactions of matter, namely the strong and weak nuclear interactions, are also gauge interactions, a property that has been hidden by confinement for the strong interactions and by spontaneous symmetry breaking for the weak ones. ... The aim of the present monograph is to provide a review of the group structure both of the non-abelian gauge theories themselves and of their spontaneous symmetry breaking.

*The Dawning of Gauge Theory*published by

*Cambridge University Press*in 1997. The publisher gives this description:-

TheDuring the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage(1916-1956)the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge invariance. In the second stage(1960-1975)it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions(both weak and strong)and thus provided a universal framework for describing all known fundamental interactions. In this work, Lochlainn O'Raifeartaigh describes the former phase. O'Raifeartaigh first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing here for the first time in English, notably by Weyl, Schrödinger, Oskar Klein, and London in the pre-war years, and by Pauli, Shaw, Yang, Mills, and Utiyama after the war. The articles illustrate that the reassessment of gauge-theory, due in a large measure to Weyl, constituted a major philosophical as well as technical advance.

*American Journal of Physics*reviewed the book:-

We should mention O'Raifeartaigh's collaborations with scientists from Eastern Europe, especially Hungary, Poland and the USSR, throughout the late cold war. Many were able to make research visits to the Dublin Institute for Advanced Studies. In particular there were physicists such as J Balog from the Central Research Institute for Physics, Budapest, Hungary, L Fehér from the Bolyai Institute, Szeged, Hungary, P Forgacs from the Central Research Institute for Physics, Budapest, Hungary, and P A Horváthy now in Tours, France. Fehér and Horváthy dedicated a 2009 electronic version of their 1989 paperThe book thus performs a double service: it offers a rewarding description of the development of the gauge symmetry idea that is complete even without the original papers, and it makes those original papers readily accessible to physicists and mathematicians. ... This book represents an important contribution to the history of fundamental ideas in physics.

*Applications of chiral supersymmetry for spin fields in self-dual backgrounds*written with O'Raifeartaigh to "our late teacher, collaborator and friend".

O'Raifeartaigh received several major honours for his outstanding contributions including election to the Royal Irish Academy in 1963, election as a fellow of the Institute of Physics in 1990, election to the Academia Europaea in 1991, awarded the prestigious von Humbolt Research Award in 1996 and the Eugene Wigner Medal in August 2000. The Wigner Medal, designed "to recognize outstanding contributions to the understanding of physics through group theory" was awarded for his:-

An international symposium, 'Symposium on Non-Perturbative and Symmetry Methods in Field Theory', was held in Budapest in June 2006 to celebrate O'Raifeartaigh's life and work.... pioneering contributions to particle physics.

We mentioned O'Raifeartaigh's love of the Irish language, of the theatre and of hill walking above. He was also interested in politics and tried to put this interest to use to make a better world [3]:-

As to his character [3]:-He put his interest in international politics to good use in the cause of nuclear disarmament; along with the Nobel Laureate Ernest Walton, he helped Michael Fry found the Irish Pugwash group, bringing together physicists and experts on international affairs.

The authors of [5] write:-... he will be remembered by his colleagues as much for his humility, patience, kindness and humour as for his academic excellence.

After a short illness, O'Raifeartaigh died from liver cancer at the age of 67.He was a man of faith. His friends admired him for his simplicity, thoughtfulness, kindness, humour, and extensive knowledge of physics.

**Article by:** *J J O'Connor* and *E F Robertson*

**List of References** (10 books/articles)

**Mathematicians born in the same country**

**Other Web sites**