# James Robert McConnell

### Quick Info

Born
25 February 1915
Dublin, Ireland
Died
16 February 1999
Dalkey, Dún Laoghaire-Rathdown, County Dublin, Ireland

Summary
James McConnell was an Irish mathematician who worked on quantum mechanics and the applications of Lie groups.

### Biography

James McConnell's parents were Robert McConnell (born 1885), who was a pharmacist originally from Ballymenna, and Frances Lennon (born 1884) from Dalkey, County Dublin. Robert McConnell died when James was four years old and he was brought up by his mother. He had a terrible experience when he was five years old. James and his mother were in Talbot Street in Dublin on 14 October 1920 when there was a shootout between a British Secret Service surveillance team and Seán Treacy, one of the leaders of the Irish Republican Army. Treacy and two British agents were killed in the shootout and this traumatic experience was witnessed by the five year old James. For the rest of his life James retained a vivid mental picture of the scene and he could name every shop on both sides of the street.

McConnell was educated at the O'Connell School on North Richmond Street in Dublin. This school had been founded by the Congregation of the Christian Brothers in 1828 and was named after the Irish patriot, Daniel O'Connell. In 1932 McConnell completed his studies at the O'Connell School and entered University College Dublin. At university he studied mathematics and, in particular, he was taught by Arthur William Conway whose lectures on quantum theory and relativity inspired McConnell. He graduated in 1936 with an M.A. with First Class Honours in Mathematics. After graduating, McConnell entered the Roman Catholic seminary of Holy Cross College in Clonliffe Road, Drumcondra, Dublin. He studied there for a year undertaking training for the priesthood. Advised to continue his studies in Rome, he moved to the Pontifical Lateran University of Rome where he received the degrees of S.T.L. (Licentiate of Sacred Theology), D.D. (Doctor of Divinity) and B.C.L. (Bachelor of Civil Law). He was ordained in 1939 and completed his studies at the Pontifical Lateran University in 1940. At the same time as he was studying at the Pontifical Lateran University, McConnell was undertaking research in mathematical sciences at La Sapienza, University of Rome, and was awarded a doctorate by La Sapienza in 1941. Of course in June 1940 Italy had joined Germany and declared war on Britain and France so by the time McConnell received his doctorate Italy was allied with Germany. However, Ireland remained neutral throughout World War II so, although the war made things very difficult for McConnell, it was still possible for him to return to Ireland in 1942.

The Dublin Institute for Advanced Studies had been founded by Éamon de Valera in 1940 with the School of Theoretical Physics being one of two schools in the new Institute. Erwin Schrödinger became the Director of the School of Theoretical Physics and, in 1942, after receiving a strong recommendation from A W Conway, McConnell joined this School. In 1943 McConnell published the paper Non-Linear Quantum Electrodynamics of the Vacuum. He begins the Introduction by writing:-
This paper is a modest first step towards establishing a non-linear quantum electrodynamics, that is to say, an attempt at a quantum mechanical description of the electromagnetic field, based on Born's non linear electrodynamics rather than on Maxwell's theory. No great revelations with immediate bearing on experiments can be expected from this first step, which deals with the charge-free electromagnetic field in the first approximation (as regards amplitudes) after the linear Maxwellian case. Yet it is a step necessary for further progress. Covering ground, which in the linear approximation is still entirely trivial, it illustrates well the complexity entailed by this - or any other - non-linear theory and thus, very probably, the true complexity of the problem of quantum electrodynamics.
He ends his paper with the following acknowledgement:-
I am greatly indebted to Professor E Schrödinger for many valuable discussions and suggestions. My thanks are also due to Professor W Heitler, who suggested the introduction of radiation damping.
In 1943 McConnell and Schrödinger wrote the joint paper The Shielding Effect of Planetary Magnetic Fields (1944). They begin their Introduction as follows:-
Very much the same as in the case of Einstein's field-equations of gravitation in empty space, Maxwell's equations likewise admit of a term expressing that the potentials act also as sources of the field-the "cosmical term," as it is usually called. While in the case of gravitation anything but an extremely low order of magnitude of this term is excluded by observation, the widespread 'belief that the corresponding Maxwellian term must be of the same low order, neither rests on direct experimental evidence, nor are there strong theoretical grounds for it.
In 1945 McConnell was appointed as Professor of Mathematical Physics at St Patrick's College, Maynooth. This College has an interesting history. It was founded in 1795 as a seminary to train priests but also taught Classics, English, Irish and Modern Languages, Mathematics, and Natural Philosophy. When the National University of Ireland was founded in 1908, it was not allowed to teach theology or grant degrees in that subject. However, a few years later, St Patrick's College became a Recognised College of the National University of Ireland for Arts and Science. Professors, like McConnell, were appointed as professors in the National University of Ireland.

McConnell published three papers on Production and annihilation of negative protons (1945, 1947, 1954). These papers involved a theoretical study of the antiproton, a particle predicted theoretically by Paul Dirac in 1933 but which was only shown to exist experimentally in 1955. In 1958 he published his book Quantum particle dynamics. Ronan Sheehan writes about this book in [5]:-
Its object was to enable those who had no previous acquaintance with relativity or quantum theory to acquire sufficient knowledge of quantum mechanics, quantum electrodynamics and meson theory to understand the main features of the theory of elementary particles.
C Strachan, in [6], feels that McConnell should have gone into more details:-
Some 250 pages offer rather cramped accommodation for the development from introductory wave-mechanics to strange particle theory via quantum electrodynamics. Particularly in the earlier chapters, on Special Theory of Relativity, Introductory Quantum Theory, Wave and Matrix Mechanics, Angular Momentum, Many-particle Systems, the reviewer feels that a reader for whom these chapters are necessary will find parts of the treatment too facile to avoid perplexity. ... One can only regret that the author did not develop part or all of his subject matter much more fully.
Also in 1958 McConnell published a paper quite different to anything that he had previously worked on. This paper, published in the Proceedings of the Edinburgh Mathematical Society, was entitled Whittaker's correlation of physics and philosophy. Gerald James Whitrow writes in a review:-
In this clearly written concise survey of Sir Edmund Whittaker's writings on the philosophy of physics, the author divides Whittaker's work in this field for convenience into five divisions: neo-Cartesianism, Eddington's principle, determinism and freewill, cosmology, natural theology. With regard to Eddington's Fundamental Theory, the author makes the point that in recent years Eddington's work would have been ignored had not Whittaker focussed attention on it, and he claims that both for this and for pointing out the epistemological defects he has placed both philosophers and mathematical physicists under a debt.
This change in McConnell's interests was followed by another change of direction. In 1964-65 he gave a series of seminars on the applications of group theory to elementary particles and he wrote these up in the 111-page tract Introduction to the group theory of elementary particles (1965). Paul Roman describes the contents in a review:-
After a few ad hoc words on elementary particles in general, the $SU_{2}$ group is briefly discussed and the notion of a Lie group is introduced. The next five chapters contain a simple, readable account on the general notions concerning semi-simple Lie algebras, their root diagrams, weight diagrams, and the reduction of product representations. Chapter 8 presents a detailed explicit treatment of the $SU_{3}$ group. Chapter 9 is devoted to the 5-dimensional rotation group, and includes mention of the possibility of applying it to leptonic symmetries. The concluding chapter reviews some of the major applications of $SU_{3}$ for strong, electromagnetic, and weak interactions.
After these lectures and resulting publication, McConnell began to publish research papers on applications of Lie groups and Lie algebras to physics, for example: Group theoretical study of leptonic processes (1965); Multiplicities in weight diagrams (1966); Properties of the exceptional $G_{2}$-Lie group (1968); The general linear group GL(4) and the Lie group $C_{2}$ (1969); and Graph theory of weight multiplicities (1970). After these papers, he published the 164-page tract Weight diagrams and their application to the reduction of representations of the general linear group (1971). Albert John Coleman (1918-2010), at that time Head of the Department of Mathematics and Statistics at Queen's University, Canada, writes in a review:-
The first half of this brochure is devoted to a detailed and elaborate discussion of the weight diagrams of representations of the simple Lie groups of rank two: $A_{2}, B_{2}$ and $G_{2}$. A graphical method is developed for obtaining the multiplicities of the weights in an irreducible representation starting from a dominant weight. In the remainder the author studies representations of the general linear group over the complex numbers, $GL(n, \mathbb{C})$ for $n > 2$, and the reduction of such representations when the group is restricted to a subgroup of rank two.
At St Patrick's College, Maynooth, McConnell took on some administrative duties. He was Dean of the Faculty of Science from 1957 to 1968 and Registrar of the College from 1966 to 1968. During this period he took study leave which allowed him to be a visiting professor at Fordham University, New York in 1959-60 and a visiting professor at Laval University, Quebec in 1964. While at Fordham University he worked with Joseph Y Shapiro and they wrote the joint paper Covariant statistical treatment of antiproton annihilation which was published in 1963. In 1968 McConnell was appointed as a Senior Professor in the School of Theoretical Physics of the Dublin Institute for Advanced Studies. He served as Director of the School from 1969 to 1972. In 1980 he published the book Rotational Brownian motion and dielectric theory. Raymond Streater writes in [7]:-
This book has a dual interest; one, according to the foreword, is to give an exposition of the theory of dielectrics that will guide experimenters to set up the critical experiment to test the substantial body of the theory described here. A second use for the book is to provide probabilists with hard but clearly interesting problems in stochastic differential equations and which call for a more rigorous treatment.
McConnell received many awards for his outstanding contributions. He was elected to membership in the Royal Irish Academy in 1949, serving as its Secretary from 1967 to 1972. He served as Chairman of the National Committee for Mathematics of the Royal Irish Academy from 1960 to 1964, and Chairman of its National Committee for Physics from 1965 to 1968. He was a founder member of the European Physical Society in 1968 and served on its Council from 1969 to 1971. In 1986 he was awarded the Boyle Medal by the Royal Dublin Society. He was elected to the Pontifical Academy of Sciences on 25 June 1990. Pope John Paul II made him a Prelate of Honour in the following year.

Ronan Sheehan, a lawyer and friend, described McConnell's sad final years in [5]:-
In September 1992, my father died. A couple of days later, I walked down the aisle of the same church to where Fr McConnell was standing at the altar-rail. He wasn't looking very well himself. ... I had taken instructions from him some time before to draft his will and I had presented it to him for execution at the Institute for Advanced Studies on Burlington Road. He bequeathed his intellectual property to 'Propaganda Fidei'. Shortly after my father's death, Fr McConnell's descent into dementia commenced. Unhappy was the day I made an application to the High Court to make this mathematical genius a ward of court and myself guardian of his person and property, including intellectual property. I knew his book had been taught in Princeton, in Beijing, in Cracow. Where else? ... What precisely were my duties in the matter? My responsibility did not last long enough to make answers to these questions an obligation. He died soon after. Responsibility for the management of his property passed to his executor.
We note that 'Propaganda Fidei', now known as the Congregation for the Evangelization of Peoples, is based in Rome and organises all the missionary activity of the Catholic Church.

The author of [1] writes:-
James McConnell was a friendly, unassuming and generous man, who was full of vitality and had an infectious enthusiasm for all his undertakings. He was sustained in his late years of failing health by his faith and the devoted care of the Carmelite Sisters for the Aged and Infirm at Our Lady's Manor, Dalkey. Requiescat in pace.

### References (show)

1. Mgr James Robert McConnell, The Irish Times (Tuesday, 6 April 1999).
3. James Robert McConnell, The Royal Dublin Society. http://www.rds.ie/index.jsp?a=778&n=245&p=182
4. S Rozental, Review: Quantum particle dynamics, by J McConnell, Nuclear Physics 14 (4) (1960), 697.
5. R Sheehan, Sub Nomine Columbae / In the Name of Columba, Field Day Review 8 (2012), 181-206.
6. C Strachan, Review: Quantum particle dynamics, by J McConnell, Mathematical Reviews, MR0102348 (21 #1141).
7. R Streater, Review: Rotational Brownian motion and dielectric theory, by James R McConnell, Mathematical Reviews, MR0625298 (83f:82001).