# 10. Cambridge

*“Where there is much desire to learn, there of necessity will be much arguing, much writing, many opinions; for opinion in good men is but knowledge in the making.”* – John Milton, Areopagitica.

Jim took up the post of Lecturer in the Faculty of Mathematics at Cambridge in January 1950, receiving his M.A. in March. In the summer Jim, Glen and daughter Elizabeth moved to a flat on Hills Road, the main road running southeast from the centre of Cambridge. As in Manchester, they rented this place and it was adequate to their needs for the two years they spent there. It was also conveniently placed, in fact within walking distance of the university. During 1951 Jim and Glen calculated that now, with a reasonable salary from Jim’s lectureship, they could afford to buy a place of their own. They spent some time looking around at what was available and opted for a house on a quiet residential road off Histon Road, on the north side of Cambridge. There was an extensive garden behind the house and behind that there were allotments for vegetables.

In 1950 the senior people in Theoretical Physics at Cambridge were Paul Dirac and Nicholas Kemmer. Kemmer, from St. Petersburg, had studied at Göttingen before taking his doctorate at Zürich (under Wolfgang Pauli). Aside from two years spent in Canada, he had been at Trinity College since 1940 and had been appointed Lecturer in 1946. Dirac’s lecture courses for part III of the mathematics tripos on quantum theory were complemented by Kemmer’s course on nuclear physics, Mrs. Jeffreys’ course on atomic theory, and a course by Harold Jeffreys, the astronomer and geophysicist.

In Mathematical Physics, Douglas Hartree was the professor. Originally a Cambridge man, he had overlapped with Jim for a year at Manchester and a friendship had developed. The Hartrees visited Jim and Glen at home on more than one occasion, though Douglas died in 1958. Hartree was a kind, friendly man, who would always convey his interest in whatever the Hamilton children were up to.

At the Cavendish Laboratory, Ernest Rutherford had again (as at Manchester University) been succeeded by Lawrence Bragg. Bragg had proposed Otto Frisch for a Trinity College fellowship, Frisch had duly been elected and had held the Jackson Chair of Physics since 1947.

There were also several highly promising young mathematicians and physicists. Richard Dalitz had left Cambridge for Birmingham in 1947, after only one year of his Ph.D., mainly because there was no research advice given to Cambridge students at that time. Remaining at Cambridge and obtaining their Ph.D.s in 1950 were Paul Matthews (under Kemmer) and Richard Eden (under Kemmer during Dirac’s absence in 1947-8, then Dirac). Initially Jim overlapped with Matthews only until August 1950 when Matthews went to Princeton, although Matthews returned for the year 1951-2 prior to accepting a lectureship at Birmingham. Eden had won the Smith’s Prize for the most outstanding pre-doctoral contribution to physics in 1949 for two papers on Heisenberg’s S-matrix and he stayed on at Cambridge as a fellow and director of studies in mathematics at Clare College, working on quantum field theory in a similar research area to Jim. Eden recalls that Jim’s willingness to interact with students and make suggestions about research were well received.

Abdus Salam was a Ph.D. student at the mathematics faculty when Jim arrived (Salam had started in the physics department in 1948, but changed to the mathematics faculty in January 1949, where he was nominally supervised by Kemmer, though in practice he had much more help from Matthews). Also there were first year Ph.D. students John Polkinghorne (under Kemmer), John C. Taylor (under Eden), Denys Sciama (Diracs’ last postgraduate student), and Roger Phillips (possibly under Jim’s supervision). Another of the students at this time was Angas Hurst, from Australia, who worked for his Ph.D. during Jim’s first three years at Cambridge. It is quite likely that Jim was Hurst’s Ph.D. supervisor. When Eden went to Princeton in January 1953, it is also likely that Jim assisted with the supervision of Gerald Rickayzen (this would have ensured continuity as Jim and Richard Eden had been working on similar topics). Salam took over the supervision of John C. Taylor after Eden, though Jim advised him unofficially.

Gerry Brown recalls that he first met Jim in 1952 (Gerry had only the previous year published his work with Geoff Ravenhall on the self-ionization of the vacuum). He and his student, Sheila Brenner, were visiting Cambridge in order to use EDSAC I, the computer developed under Maurice Wilkes in the Mathematical Laboratory. Jim and Gerry had met and discussed their respective research. Gerry’s recollection is that : “He [Jim] was quite interested in my research and highly complimentary.” Jim invited Gerry and Sheila home for supper one evening and so began a friendship between Jim and Gerry which would be renewed later on in Copenhagen.

Also in 1952, Jim’s paper ‘Real and Virtual Processes in Quantum Electrodynamics’ (Proc. Camb. Phil. Soc. 48, p.640), was published. This paper was probably written in the Easter term of 1951 and is the first time that Jim uses the term ‘S-Matrix’ to describe the scattering matrix, relating the initial state and the final state for an interaction between particles. He refers to the “S-Matrix formulation of quantum electrodynamics, as developed by Richard Feynman (1950, Phys. Rev. 2, 80, p.440) and Freeman Dyson (1949, Phys. Rev. 2, 75, p.486, p.1736)” and comments : “any graph of the type introduced by Feynman and Dyson can be expressed as the sum of graph parts.” In his paper Jim shows how any *real *graph part can be expressed as the sum of its constituent *virtual* parts. The paper also refers to recently published works by Eden and by Hurst, acknowledging discussions with these two and Matthews.

Early S-Matrix theory had been developed by two men in particular, Heisenberg and Møller. It was thought that the strong interaction could be understood through the analytic properties of the S-Matrix. In December 1944 the OSS agent Berg, with a gun in his pocket, had attended a lecture by Werner Heisenberg in Zürich, allegedly authorised to kill Heisenberg if there was even a whiff of talk about developing an atomic bomb. There wasn’t – Heisenberg delivered a lecture on S-Matrix theory and Berg’s gun stayed in his pocket. In his book ‘The Theory of Elementary Particles’ (p.188), Jim recommends that for the S-Matrix, readers should refer to Heisenberg from 1943 (Zs.f.Phys. 120, p.513 and p.673) and Christian Møller, from 1945 and 1946 (K. danske videnske. Selsk. Skr. 23, no. 1, 26, and no. 19).

In his 1953 paper ‘Steady States and the S-Matrix’ (Proc. Camb. Phil. Soc. 49, p.97), discussing the relation between the bound state of two interacting particles and the S-Matrix, Jim again refers to work by Feynman and Dyson, and now to work by Salpeter and Bethe (1951, Phys. Rev. 2, 84, p.1232), and Schwinger (1948, Phys. Rev. 2, 74, p.1439). Also Gell-Mann’s name appears, in a collaboration with Low (1951, Phys. Rev. 2, 84, p.350).

This was followed by another publication in 1953 : ‘Convergence in the Intermediate Representation’ (Proc. Camb. Phil. Soc. 49, p.642). The paper “is intended to be a contribution to the search for a suitable expansion for meson theory. Perhaps the simplest expansion method, other than in powers of the coupling constant, is that which arises from the intermediate representation which was invented by Dyson.” The reference is to Dyson’s 1951 publications in Phys. Rev.(2) 82, p.428 and Phys. Rev.(2) 83, p.608.

A third publication in 1953, ‘Fredholm Theory of the S-Matrix’ (Phys. Rev. 91, p.1524), again discusses convergence in the S-Matrix and refers to recent work by Salam and Matthews using the Fredholm Theory (1953, Phys. Rev. 90, p.690) : Jim acknowledges sight of the unpublished manuscript.

Jim was elected fellow of Christ’s College in March 1953. The fellowship would have been by invitation and likely came about because Jim had already been helping the college by giving supervisions in applied mathematics to some of the students : the director of studies at Christ’s College at that time was Mr. Steen, who was a pure mathematician and would have appreciated Jim’s assistance with the applied mathematics side (it is probable that when Jim arrived in 1950, Steen had taken the initiative to ask Jim to help supervise his students). The fellowship involved an extra workload – in addition to his lectures in the Faculty – some six hours a week of supervisions to the mathematics students of the college and possibly further time spent in assisting other science students with their mathematics studies. Another thing about the fellowship was that Jim now had a college room. Since moving from Manchester, where he would have shared an office or at least had a desk adjacent to the physics laboratory, Jim must have felt really quite isolated at Cambridge, without either college room or university office. Now, as a fellow, he would sometimes be expected to dine at ‘High Table’. Famine or feast.

Richard Eden recalls that the lack of common research areas, for staff or research students, continued for some time and was not properly resolved until 1960 when a new top floor was built on the Austin Wing of the (old) Cavendish Laboratory. One might ask how a faculty could organise seminars when there was nowhere to hold such meetings. The answer is that the faculty didn’t organise them. There were no theoretical physics seminars until the graduate students themselves started them in 1948. Initially the seminars were held in rooms begged or borrowed.

Eden would later, in 1964, become one of the founding fellows of Clare Hall. The idea was conceived out of similar concerns : that adequate common meeting areas had not been provided hitherto and that there was not sufficient provision for visiting researchers. As was the case with the founding of DIAS in 1940, the inception of Clare Hall was partly inspired by the Institute for Advanced Study in Princeton (founded in 1930). Eden spent nearly two years at Princeton in 1953-4 then took a senior lectureship at Manchester in 1955 before returning to Cambridge in 1957. During Jim’s time at Cambridge the two became friendly and Eden recalls meeting Jim’s family during the 1950s. Richard Eden also recalls that he and his wife, Elsie, would sometimes meet up with Jim and Glen many years later, after Jim had retired and moved back to Cambridge.

Kemmer left Cambridge in 1953, to become Professor of Mathematical Physics at the Tait Institute, Edinburgh. Ron Shaw, who was a research scholar at Trinity College during the years 1952-5 and had been under Kemmer, believes that he may possibly have been under Jim’s supervision for a few months, prior to Salam becoming his research supervisor. Shaw preferred to work on his own and does not recall discussing his research with Jim, “…except perhaps to say that it was going OK.”

Another man who Jim came into contact with at this time was John Gerald Taylor. John G. Taylor was a research student at Christ’s College and under Jim’s supervision for 1953-4, then realising that his mathematical interests had deepened, moved to John’s College under Frank Smithies. John G. Taylor, later to achieve distinction at King’s College London, recalls the excitement of this period at Cambridge : “I remember Jim’s enthusiasm and his papers which I found very stimulating. His book [‘The Theory of Elementary Particles’] was also excellent.”

Jim’s first son, Andrew, was born in November 1953. When still quite young, the boy had been ill and perhaps delirious for a day or two. He must have recovered overnight and had woken up with a clear mind as Jim entered his bedroom next morning. Jim asked how he was feeling and said some sympathetic things, then went on to say that the boy had suffered with diarrhoea. That was a term unfamiliar to the boy, whose response was that there was nothing wrong with either of his ears. This had Jim laughing out loud and attempting to explain the joke to his young listener.

Jim was generally good humoured with the children, though there were times when their misdemeanours exasperated him : on these occasions, as much as anything, he appeared to resent the unnecessariness. He would say, “There’s no need for this” or “There’s no sense to this.” At these times Jim could appear frighteningly stern. The first two children were on the wrong end of Jim’s temper more than a few times, but they deserved it. One just had to stand there and let it blow itself out. But then later on in the day, or the next morning if the row had been in the evening, Jim would be just the same as usual and one started again with a clean sheet. The overriding recollection from this time is of a cheerful and affectionate man; particularly characteristic was Jim’s warm “Hello”, and welcoming smile. This was typical of him throughout his life.

Glasgow hosted a conference on Nuclear and Meson Physics in 1954. It’s not known whether Jim attended, yet it seems unlikely that he would have missed it. The northern section of the train journey to Glasgow would have brought back memories of his journeys with Grandma Mackay.

In 1955 the paper ‘Bound State Representation’ (Proc. Camb. Phil. Soc. 51, p.103) was published, a collaboration by Jim and Abdus Salam. After obtaining his Ph.D. Salam had returned to his homeland, which had become Pakistan during his absence, for a brief period before taking up a Lecturer’s appointment back in Cambridge in 1954. Jim thought that Salam was pretty good and so must have some others, for Salam became Professor of Theoretical Physics at Imperial College, London in 1957.

‘Bound State Representation’ hints at an emerging difficulty in particle physics. “Two main approaches to the problem of bound states in quantum field theory have been made…”, in the first approach “…the original Tamm-Dancoff method suffered from serious difficulties arising from vacuum self energy…”, and in the second “…the equation of Salpeter and Bethe can be derived either directly, as Gell-Mann and Low (1951, Phys. Rev. 84, p.350) did, or by means of Feymann amplitudes following Matthews and Salam (1953, Proc. Roy. Soc. A, 221, p.128). Gell-Mann and Low’s method gives a kernel which is expressed as a power series whose convergence has not been proved. In Matthews and Salam’s method the equation contains a remainder whose size has not yet been investigated.”

Quantum field theory had become established in 1926, through the work of Born, Heisenberg and Jordan. A year later Dirac had produced his comprehensive theory of electrodynamics. These theories gave a framework for understanding particle physics from a quantum mechanics viewpoint. The theory was developed by Jordan and Pauli, then Bohr and Rosenfeld, and Dirac, to encompass Einstein’s relativity theory. Into the 1940s it had appeared that the theory was still lacking : there had been a problem with ‘divergence’ – where application of the theory had given nonsensical results in calculations of physical quantities. This had been resolved by Bethe, Tomonaga, Schwinger, Feynman and Dyson through a process of renormalization, but there would still be further problems.

Could the ‘strong interaction’ (or at that time the ‘strong force’, postulated to be a force strong enough to overcome the electric repulsion by protons) be understood in terms of Quantum Field Theory ? Still in 1955, Jim’s paper ‘Functional Analysis and Strong-Coupling Theory’ (Phys. Rev. 97, p.1390), examines the relation of functional analysis to the Hamiltonian approach to strongly interacting quantized fields.

Into the 1950s the strong interaction had become termed the pion-nucleon interaction. In 1947 it had been shown that the particles originally thought to be mesons were in fact decay products (‘muons’); the true mesons, mediators of the strong interaction, were termed ‘pions’. ‘Nucleon’ is a collective term for the proton and neutron, the heavy nuclear particles.

Jim had three published papers during 1956. ‘Centre of Mass State Vectors’ (Proc. Camb. Phil. Soc. 52, p.97), opens : “The covariant formulation of quantum field theory, in spite of its success in electrodynamics, has not been particularly useful in explaining either pion-nucleon scattering or the structure of the nucleon itself. At the other extreme of theories, the phenomenological explanations based on the simplest of physical concepts have had a fair measure of success, and the structure of the nucleon has been discovered to be considerably more complicated than it was generally thought to be. Arguments based on a few fundamental invariance properties and ideas borrowed from the resonance theory of the compound nucleus are commonly used in describing nucleon-pion interactions.” The paper goes on : “One of the important concepts used in discussing high-energy phenomena is the angular momentum in the centre-of-mass system, and it is the purpose of the present paper to derive state vectors which describe this angular momentum. The general methods of field theory probably provide the clearest language for discussing processes in which particles, or pairs of particles and anti-particles, may be created or destroyed; so it seems desirable to express the properties of the centre-of-mass system in field-theory terms, in the hope that it may help to relate the phenomenological and the sophisticated theories.”

‘Isotopic Spin and High Energy Collisions’ (Suppl. Nuovo Cimento 4, p.803) opens : “It is becoming increasingly important to analyse the *intermediate *or *compound *states occurring in high-energy pion-nucleon scattering…the present paper puts forward suggestions for dealing with the isotopic spin components of these intermediate states.” The paper ends with ‘Interventi e Discussioni’ which comprises :

“- B. Touschek : Is the pion-state referred to short-lived or long-lived ?”

“- J. Hamilton : Definitely short-lived.”

Mean lifetimes for charged and neutral pions are quoted at the time of this writing as 2.60×10^{-8} second and 0.84×10^{-16} second respectively.

Hans Bethe visited the Cavendish Laboratory in 1955-6 on leave of absence from Cornell. Bethe had obtained his doctorate at Munich (under Sommerfeld) but had left Germany in 1933 when he was dismissed by the Nazis from his post at the University of Tübingen. After two years at Bristol (where he had engaged in collaborations with Rudolf Peierls and Walter Heitler), he had departed for Cornell. In Los Alamos he had headed the Theoretical Division and back at Cornell his work on electrodynamics had paved the way for Feynman and Schwinger. Into the 1960s his attention would turn to theoretical astrophysics, resulting in his discovery of stellar nucleosynthesis. Into the 1980s and 1990s he would collaborate with Gerry Brown in work on supernovae, neutron stars and black holes; Bethe was also remarkable for a research career that extended into his 90s.

‘Anti-Proton Annihilation’ (1956, Nuovo Cimento 4, p.1) was a collaboration between Jim and Bethe. The anti-proton had recently been discovered by Chamberlain, Segre, Wiegand and Ypsilantis (1955, Phys. Rev. 100, p.947) and this allowed the opportunity to obtain information about nucleon-pion forces quite distinct from nucleon-nucleon and nucleon-pion scattering. After Bethe returned to Cornell, Jim nominally (until Easter 1957, when Richard Eden returned to Cambridge) took over the supervision of Jeffrey Goldstone, who had been under Bethe for the first year of his Ph.D. work.

In addition to these publications Jim was also preparing a larger manuscript. It was first suggested in 1954 that he should collate the notes from the various courses of lectures which he had been delivering at Cambridge into a book. During the years to 1958 he found the additional time required to achieve this, and the resulting text ‘The Theory of Elementary Particles’ (Oxford Clarendon Press) was published in 1959. Even during the time Jim was working on the manuscript, there were considerable new developments in the subject which only made his job more difficult. Nevertheless the completed book became a staple text for a generation of physics students wishing to study elementary particles and was reprinted in several languages.

By the mid-1950s Jim was a frequent visitor to AERE, Harwell. The establishment had been set up in 1946 under Cockcroft, a man famous for his research at the Cavendish Laboratory under Rutherford. John Cockcroft and Ernest Walton are commonly credited as the first to ‘split’ the atom : in 1932 they bombarded Lithium with accelerated protons and broke it, producing Helium. Cockcroft had established good experimental facilities at Harwell and was attracting many physicists : the period 1950-1965 was described by Alan Cottrell as “Harwell‘s Golden Age”. Jim would spend up to a week at a time there and sometimes Glen and one or other of the children would take up temporary accommodation in a nearby cottage.

One of the men regularly working at Harwell was Otto Robert Frisch. The Frisch family would occasionally visit Jim‘s family at home, though it was more often just Ulla and the children. The writer recalls that Jim would use ‘Robert’. Frisch had always been ‘Robert’ until his time at Los Alamos, where he had discovered that “the place was lousy with people called Robert.” When asked his first name he had replied honestly “Otto”, which had stuck.

Jim’s son could never understand anything Otto Robert said, for one thing he retained a heavy Austrian accent and for another he would usually be talking physics. In fairness to Frisch, he did observe social etiquette but was simply keen to move on to a conversation which interested him more. There were other renowned physicists who completely disdained any kind of small talk. As a host Jim would be warmly welcoming and seemingly had as many general topics of conversation as were required to put his guest at ease. He wouldn’t usually press a discussion of physics, but if it was clear that a guest desired this, he’d happily oblige. He asked questions and was often content to spend more time listening than talking.

In 1956 Hans Bethe delivered a lecture at Cambridge which included a general discussion of ‘Dispersion Relations’. The term ‘Dispersion Relation’ derives from Optics studies of materials with non-constant index of refraction, the Dispersion Relation being “an integral relation connecting the real and imaginary parts of the refractive index”, relating the refractive and absorptive parts of the index. Kramers and Kronig demonstrated in 1926 that the absorptivity determines the refractivity (J. Opt. Soc Amer. 12, p.547). For elementary particle collisions there are analogous relations between the real and the imaginary parts of the scattering matrix. In ‘The Theory of Elementary Particles’ (p.335) there is reference also to the term ‘Dispersion Theory’, though the context implies that this term was borrowed from Bethe.

In ‘On Mesons and Methods’, Jim gives the following account of dispersion relations : “A most powerful and precise method of analysis was provided by partial wave amplitude dispersion relations. Dispersion relations are based on three principles:

a) *causality*. In its general form, a two-body scattering amplitude regarded as a function of energy can not have any singularities in certain large regions of the complex plane;

b) *unitarity*, which gives important constraints on scattering amplitudes;

c) *crossing symmetry*, which was originally noticed in the close relation between bremsstrahlung [electromagnetic radiation emitted when a charged particle changes velocity] and e^{+} e^{–} photoproduction on a nucleus [refers to H.A. Bethe and W. Heitler‘s 1934 publication (Proc. Roy. Soc. A 146, p.83)].”

He finishes : “They [dispersion relations] can be of great value when they are properly used.”

Murray Gell-Mann and Marvin Goldberger had illustrated the use of crossing symmetry in 1954 (Proc. 4th Ann. Rochester Conf., p.26). Using causality, Goldberger had in 1955 (Phys. Rev. 99, p.979) derived dispersion relations for forward pion-nucleon scattering, and their extension to non-forward scattering soon followed. The importance of unitarity (in all situations the sum of the squares of the amplitudes must be equal to 1) is later demonstrated by Stanley Mandelstam in his papers of 1958 (Phys. Rev. 112, p.1344) and 1959 (Phys. Rev. 115, p.1741 and p.1752). By using these principles it became possible to use dispersion relations to provide a dynamical theory of strong interactions.

For an introduction to the subject of dispersion relations, Jim’s article ‘Dispersion Relations for Elementary Particles’ (‘Progress in Modern Physics’, vol. 8, p.143, Pergamon 1960) should be mentioned. On causality, using the example of the scattering of light by an atom, the article provides a proof that scattering cannot commence before the incident wave reaches the atom. The article also develops the topic of sum rules, which are “most commonly used to check the accuracy and consistency of the data which have been accumulated.”

Addressing the use of dispersion relations for elementary particles, Jim writes : “In recent years a large class of new techniques, which are generally known as dispersion relations, has been developed in order to study the properties and the interactions of the elementary particles. The great incentive for this development is that dispersion relations can give accurate results for very strongly interacting particles as well as for weakly interacting particles, whereas the older methods of quantum field theory are, in general, quite inadequate for treating strongly interacting particles (selection rules apart).”

“Most theoretical physicists believe that dispersion relations, when they are used correctly, provide a very precise and powerful tool in elementary particle theory. Some theorists will go much further by suggesting that the dispersion relations themselves will eventually give a complete solution of field-theory problems, i.e. they will enable us to calculate all cross-sections, transition probabilities and particle form-factors in terms of the masses and coupling constants of the elementary particles. In other words, the scope of the information given by dispersion relations may be progressively increased until they can answer all physically meaningful questions. At the present time this suggestion may seem to be somewhat extreme, or possibly somewhat rash. We shall only comment that the history of dispersion relations shows a strong tendency in this direction.”

Jim had collaborated with Bethe on ‘Anti-Proton Annihilation’ and their mutual interest culminated with the suggestion that Jim should seek leave of absence from Cambridge in order to work as a research associate with Bethe for a year at Cornell (where Bethe had been professor since 1939). Jim, who was by now considered expert on dispersion relations, was to deliver a course of lectures on the subject at Cornell and it would also be an opportunity for him to acquaint at first hand with research methods in the United States. Funding was provided in part by the joint program of the Office of Naval Research and the U.S. Atomic Energy Commission. As Jim’s appointment at Cornell would be for a full year it was also arranged for his family to accompany him and accommodation was organized for them in Ithaca.

There were two other connections with Bethe : Bethe’s wife, Rose, was the daughter of the man Jim had worked with at Queen’s, Paul Ewald. Bethe may well have heard about Jim ‘through the family’ at that earlier time. Also it is likely that Jim and Bethe would have known about each other through Walter Heitler. Jim’s high respect for Bethe would later be illustrated in ‘Classical Pion Physics’, an article he contributed to ‘Perspectives in Modern Physics’ (ed. Marshak, Wiley 1966), a collection of essays in honour of Bethe on the occasion of his 60th birthday. Jim starts : “Hans Bethe has the art of making clear and vivid pictures of the processes which go on in the strong interactions, and it was therefore a great pleasure to be asked to write such an article on one aspect of strong interactions for this festschrift. Before getting down to the subject, I wish to thank him for much instruction and for many interesting and valuable discussions covering a wide range of physical phenomena.”

This also was a time of significant change in the mathematics faculty. Richard Eden returned to Cambridge in 1957 (resuming his role at Clare and taking up the lectureship in mathematics left vacant when Salam went to Imperial College). By then Jim had become secretary of the faculty board of mathematics, with responsibility for arranging the lecture timetable and examiners (with guidance from the very efficient secretary typist – she had been in the job for a number of years and in practice one only needed to heed her advice). Together with George Batchelor, Jim had been planning to set up a department for applied mathematics within the faculty of mathematics. During the spring of 1957, Eden started to introduce changes to the mathematics tripos which would lead to a mathematics with physics option for students effective from 1958-9. In order to allow implementation of Eden’s changes, Jim and Batchelor agreed to postpone their changes until 1958, which also conveniently allowed Jim to take his year at Cornell without disrupting the planning process.

The family travelled across the Atlantic by liner in late August 1957, a crossing memorable for the ship sailing into the periphery of a hurricane. Jim took the children onto the covered deck running along the side of the ship, in order to better appreciate the mountainous waves. Jim had become accustomed to rough seas, first as a youngster accompanied by Grandma Mackay on crossings of the North Channel and later during his time in operational research, and was not the least perturbed by the conditions. His ease transmitted to the children.

There was not much time off during Jim’s first six months in Ithaca. In addition to his lectures and research at Cornell, he also spent some time at Brookhaven National Laboratory in Upton, N.Y. During the second half of his stay he took the family on two long journeys, one of a few days down to Wilmington, N.C. at the end of March 1958 – presumably this was the Easter holiday period – and the other, in June, a longer trip over to Los Alamos and then to Berkeley. Jim hired cars for these journeys and didn’t mind the long drives.

Los Alamos, as Glen put it had : “All the material trappings of a town, set down in desolate country, miles from anywhere, ten different Christian churches and one Jewish, but no soul…” in contrast to Santa Fe “…only one true Catholic church and plenty of soul.” From Santa Fe the route passed Grants, at 6,470 ft, which proclaimed itself ‘The Uranium Capital of the World’ but was otherwise unremarkable. At Berkeley Jim was able to talk for a while with physicists from the University of California and the family were allowed to walk around the Bevatron. Meson theory had continued to develop during the 1940s. In the days before particle accelerators, the only way to closely observe meson behaviour was by photographic emulsion located near the peaks of high mountains. In 1947 the first true mesons were observed by Powell, Lattes and Occhialini. The true meson, or pion, left a ‘double meson’ track on the film. One track was from a pion, the other was from its decay product, a muon. The ‘mesons’ previously observed had in fact been the decay products. Subsequent experiments showed that muons did not participate in the strong interaction and are more recently not even considered to be mesons at all. The pion, however, does mediate the strong interaction and in 1948 Lattes and Gardner had first achieved artificial production of pions here at Berkeley, by bombarding carbon atoms with alpha particles.

Jim spent July and August re-drafting chapters VI and VII of ‘The Theory of Elementary Particles’ in order to incorporate new information on dispersion relations and the pion-nucleon interaction, and to cope with “the difficult aftermath of the great parity and beta-decay revolution of 1957-8.” ‘Parity’ concerns the relation of something to its mirror-image : the view had been that there is symmetry in nature. In 1954 Richard Dalitz had discovered seemingly unsymmetrical results for K meson decay and by 1956 T.D. Lee and C.N. Yang had proven that this was an effect of the ‘weak interaction’ (a particle force about 10^{-13} times less than the strong force). Another late addition to the book was a reference to ‘strangeness’, Murray Gell-Mann’s recently proposed theory which he would later (1964) develop into the concept that all previously identified sub-atomic particles are composed of quarks. Rosenfeld’s warning to an author who would attempt to write a comprehensive text on a rapidly developing subject may have echoed in Jim’s mind : “…from the start he must give up any hope of producing an entirely up-to-date survey…”. Yet there was still time for the family, including a brief outing to a major league baseball game at Fenway Park.

‘Pion Scattering and Dispersion Relations’ (1958, Phys. Rev. 110, p.1134) examines a discrepancy between experimental data obtained by Puppi and Stanghellini (1957, Nuovo Cimento 5, p.1305) and dispersion relations for the forward scattering of negative pions as developed by Goldberger, Miyazawa and Oehme (1955, Phys. Rev. 99, p.986). “The discrepancy cannot be removed without contradicting one of the several apparently accurate experimental results. A relation to check charge independence is suggested.” Jim acknowledged valuable discussions with Bethe.

In ‘Pion Scattering and Dispersion Relations’ (1958, Phys. Rev. Letters, 1, p.146) with H.Y. Chiu, Jim cited work by Korenchenko and Zinov which appeared to reduce the discrepancy. This work also refers to a paper by G.F. Chew et al. (1957, Phys. Rev. 106, p.1337). Geoffrey Chew was appointed to the chair at University College Berkeley in 1957 and, as one of the leaders of the S-Matrix approach to understanding the strong interaction, he developed a strong theory group at Berkeley. Chew’s 1966 book ‘The Analytic S-Matrix’ would become very influential for some years.

‘Dispersion Relations for p-n scattering’ (1959, Phys. Rev. 114, p.1170) deals with extending N.N. Khuri’s derivation (1957, Phys. Rev. 107, p.1148) of dispersion relations for the Schrödinger equation. Jim acknowledges Goldberger for several valuable discussions.

The other thing about Jim’s year at Ithaca was that it gave him the opportunity to invite his parents over for a visit to North America. Although there had been various visits to Britain by the Mackays who had emigrated, the writer believes that this was the only time Jessie crossed the Atlantic. Joe and Jessie were able to spend a short time with the family at Ithaca during the summer of 1958, before travelling on to Canada to visit Jessie’s siblings and their families. Joe later wrote to Jim : “Another few months would have been too late.” In September the family returned to England and almost immediately visited Glen’s parents in Verwood : Glen’s father was recovering from a heart attack he suffered while she was in America.

Jim returned from Cornell with a plan for a major research programme on the pion-nucleon interaction. Quantum field theory had contributed greatly to the understanding of quantum electrodynamics, but could not be used to explain the strong interaction (a perturbation expansion did not make sense). It was thought that the strong interaction might now be better understood on the basis of general properties of the quantum amplitudes by the use of dispersion relations.

Jim took on 4 research students in 1958 : Bill Woolcock, David Spearman, Ian Hunter and Lionel Lovitch. Prior to arranging his year at Cornell, Jim had arranged to take on Bill Woolcock as a Ph.D. student. Woolcock had graduated at Queensland University and had been offered a postgraduate place at Clare College for September 1957. He had been advised that Jim would be the best person to supervise his research in elementary particle physics and this had all been agreed. It must have been something of a disappointment for Bill to have to put his own plans on hold for a year, but he generously points out that “David Spearman and I arrived at just the right time for us. Jim set us both to work on the pion-nucleon system and we all worked together to understand all that we could about it, using dispersion relation techniques.”

At this time the research group in particles and fields was housed together in an old building in Corn Exchange Street. All the research students were together in one large room, the lecturers and postdocs having individual rooms. By 1959-60, when the group was larger, some of the research students used a room in the Arts School (a room where mathematics lectures were held).

Woolcock recalls his particular research topic : “Jim asked me to sort out why the measured value of the Panofsky ratio did not agree with the pion-nucleon s-wave scattering lengths obtained from low energy pion-nucleon elastic scattering experiments (the Panofsky ratio is the ratio at threshold of the cross-sections for the processes in which a negative pion + a proton go to a neutral pion + a neutron or to a photon + a neutron). I figured out that the problem lay with the determination of the scattering length for elastic positive pion-proton scattering. Jim would not believe my suggested solution; he could be very stubborn. But not too long afterwards he came to me with new experimental data which he had just received. They showed clearly the effect for which I had already found some evidence; he had to admit that I had been right.” Out of this work ‘Low Energy Pion Phenomena’ (Phys. Rev. 118, p.291), a collaboration between Jim and Bill (Woolcock’s first paper), was published in 1960. Bill graciously points out that Jim did most of the writing. Jim also added some material on electromagnetic corrections to pion-nucleon scattering which would later turn out to be very important.

Another significant thing about this publication is that it is the first of many collaborations which acknowledge support in part by a grant from the US Air Force, European Office, Air Research and Development Command. Jim had arranged this funding through contacts made during his year at Cornell. The funding would support visits to conferences and summer schools and would also support visiting researchers at Cambridge. When Jim moved to UCL in 1960 he was able to take the funding with him, and the grant continued for the benefit of the High Energy Physics Group at UCL for a time even after Jim left there in 1964 (Bill Woolcock, who would move to UCL with Jim, administered the grant after Jim’s departure).

Jim involved David Spearman in working with him on the use of partial-wave dispersion relations for s-wave pion-nucleon scattering to obtain information about pion-pion interactions. The pion-nucleon interaction is observable experimentally, but the pion-pion interaction is not. Bill Woolcock points out that the work used s-wave phase shifts which at that time were not very well known. This work was published in 1961, in the collaboration ‘Low Energy Pion Scattering’ (Annals of Physics, 12, p.172). The paper refers to recent work by Chew, Goldberger, Low and Nambu (1957, Phys. Rev. 106, p.1337) and Mandelstam (1958 and 1959, Phys. Rev. 112, p.1344 and 115, pp.1741, 1752). Mandelstam had adapted Tullio Regge’s non-relativistic theory of 1957 into a meaningful physical theory, ‘The Mandelstam representation’, which was not based on causality but was deduced from a general hypothesis about the analytic properties of scattering amplitudes, and would be of much interest during the 1960s. In ‘Dispersion Relations for Elementary Particles’, Jim states : “the hypothesis has not been proved, but it has (so far) been verified up to fourth-order graphs in perturbation theory. The proof or disproof of Mandelstam’s hypothesis is a matter of great importance for the whole development of dispersion relations.”

Jim later recollected the early work with Woolcock and Spearman : “We thought that to an S-wave pion the nucleon looked like a small core, where pairs and other short-range processes occur, surrounded by a pion cloud. The low energy incident pion could scatter on the pion cloud, which would be about 1 fm [a femtometre is 10^{-15} metre] radius. We found some evidence supporting such a pion-pion interaction.” Jim also later referred to the explicit use of angular momentum conservation as an important step.

On his return from Cornell, Jim was once again at the core of the planning for a new department within the mathematics faculty. Richard Eden recalls joining Jim and Batchelor in the process of planning the new department, which they decided to call the Department of Applied Mathematics and Theoretical Physics (DAMTP). The new department would also include astronomers and Fred Hoyle, who was then a professor in the faculty of mathematics, would sometimes join in the discussions. DAMTP was approved by the central university committees in 1959 and Batchelor was appointed the first Head of Department. This meant that Batchelor took over the role of allocating lecturers for courses in applied mathematics, previously done by Jim as faculty secretary. Jim had always ensured to consult colleagues about any changes in their lecturing duties and his careful consideration was missed.

Despite being active on several fronts, Jim was for the most part relaxed and would find time to spend with the children. During the summers of 1957-61 he sometimes encouraged a game of cricket in the back garden. Initially these games would be with a child-sized bat and tennis ball, but as the children grew more proficient, he provided a proper bat and hard, compo ball, and bowled over-arm. One afternoon, Glen was out of the house somewhere, the ball slipped out of Jim’s hand just as he was bowling. This sort of thing happens occasionally to even the best players, but now the ball sailed in a wide, high arc straight through the small larder window, some distance away from the make-shift wicket. Jim’s initial expression of consternation gave way to a wry smile, then a chuckle. Together the players tidied up the broken glass and Jim boarded the window until such time as he could get some replacement glass cut. When Glen returned home Jim and the boy must have been looking at each other and their secret would have been ill-concealed. It didn’t take Glen long to get out of them what had happened.

Considering that Jim had been restricted in his enjoyment of games when himself a boy, where had his passion for cricket come from ? There was no first-class cricket in Ireland and the sport didn’t feature there anything like it did in England. Some Irish private schools played the game as did the universities. Yet by the time Jim lived in England he had a keen interest in the sport. He could bowl quite effectively too, a right-arm off-break spinner with a slow three step approach and a good side-on delivery stride : it seems unlikely that he hadn’t played the game previously. It would later emerge that Jim was also quite handy at table tennis and that this had been learned while he was an undergraduate at Queen’s. Between lectures he and one of his friends, Paddy Best, initially a Mathematics undergraduate in Jim’s year, would play table tennis. It’s likely that Jim also picked up cricket during his time at Queen’s.

In July 1959 Jim travelled to Kiev to attend the International Conference on High Energy Physics. After his arrival he sent the following telegram to Glen “Arrived Safely No Plug – Hamilton”. For some reason there really was a shortage of rubber in Russia. Short on rubber but long on water…

Kiev University had become well-known for its research into nonlinear oscillation, the foremost figures in this work being Nikolay Krylov and Nikolay Bogolyubov. Jim refers in ‘The Theory of Elementary Particles’ (p.346) to N.N. Bogolubov. This is the same person, his name can also be spelled Bogoliubov. Jim would later refer to Bogolyubov’s work with Dmitry Shirkov, ‘Introduction to the Theory of Quantized Fields’ (Interscience, New York, 1959). Having completed his Ph.D. in 1956, John G. Taylor had gone on to Princeton for 1956-8, where with Hans Bremerman and Reinhard Oehme, he had published a proof of dispersion relations and the famous ‘Edge-of-the-Wedge’ theorem (1958, Phys. Rev. 109, p.2178). Taylor recalls that this was much talked about at the 1959 Kiev meeting. Back as a research fellow at Christ’s, Taylor wrote up this work to gain an Adam’s prize in 1959 (shared with the team of Salam and Matthews).

Arthur Wightman had worked on what became known as the ‘Wightman axioms’ during the early 1950s – these were an attempt at a mathematically rigorous formulation of quantum field theory. The axioms suggest that there is a Hilbert space upon which the Poincaré symmetry group acts unitarily, and provide a foundation for perturbative methods. (‘Minkowski space’ represents spacetime by adding a single dimension of time to three Euclidean space dimensions, its symmetry group is the Poincaré group; David Hilbert extended the notion of Euclidean space to infinite-dimensional spaces). By applying the edge-of-the-wedge theorem in quantum field theory it is possible to construct the analytic continuation of Wightman functions.

Following the conference Jim travelled on from Kiev to Moscow before returning to Cambridge with an assortment of beautiful gifts for the family. A Russian doll for Glen and wonderful wind-up monkey cymbalists for the children. These latter artefacts, had they survived, would now be collectors’ items. On the other hand a child’s toy, still in its box, tells a sad story.

Either side of this visit to the Soviet Union, once in June and again in September, Jim visited his parents in Larne. Jessie had not been well for some time and lately had been in a great deal of pain. She bore her suffering bravely, but Jim would have known that all was not well. He took some photographs during the September visit and the last picture of the reel, from his return journey across the North Channel, was of the sun setting. Jessie died in December.

Into the late 1950s there was a hope among particle physicists at Cambridge that the experimental work at the Cavendish Laboratory would be expanded. It was hoped that Denys Wilkinson, who had been at Jesus College and become a Reader during 1956-7, would lead such an expansion and a grant was nearly obtained. There was understandably some disappointment among Cambridge physicists when Wilkinson accepted a professorship at Oxford in 1957. It is fair to say that Cambridge had not adapted its faculty appointments to match its academic distinction. Many Cambridge lecturers (including Jim) had the international status which would have made them professors elsewhere. It would be into the 1990s before Cambridge began to regard professor as a career grade.

In early 1960, although maybe late 1959, Jim had been in contact with University College, London. There was the possibility of a professorship there. After working during the war for the Admiralty Mining Establishment, Harrie Massey had resumed his work at UCL and in 1950 had become head of the Physics Department, and there was now a vacancy for a professor in the second chair. At UCL there were several active experimental groups, yet there was only one theorist interested in elementary particles, Sigurd Zienau. Massey was very much involved with a strong theory group studying atomic and molecular physics headed by Mike Seaton (who had been a Ph.D. student under Massey and Bates), but wished also to build an ‘High Energy Physics Group’, an elementary particle study group.

Jim was by now considered one of the leading elementary particle physicists and Massey always favoured appointing people with whom he was personally acquainted. It was a good appointment for both parties. Jim would also bring with him two of his group from Cambridge, Bill Woolcock and David Spearman, so the nucleus of a new study group was already provided. The appointment was provisionally agreed for September 1960. Woolcock and Spearman arranged leave of absence from Cambridge in order for them to undertake the last year of their Ph.D.s with Jim at UCL.

Jim attended a conference and meetings in Italy during April 1960 (Rome, Pisa and Genoa) and was back at Cambridge for two months prior to travelling again, this time to Geneva and Chamonix. This second trip was for Jim to lecture at the French International Summer School at Les Houches, a few kilometres west of Chamonix and the Massif du Mont Blanc. Glen and the children, who had accompanied him on the visit to Italy, remained at home during his second trip : Glen was mid-term with their third child, Patrick. It was likely between the two trips that Jim received confirmation of his appointment to the second chair at UCL. A letter from Glen to Jim in July discusses plans for Jim to take digs in London : they had decided not to move the family from Cambridge until after the new baby was born.

From September 1960 the family didn’t see so much of Jim for a while. He returned to Cambridge at weekends, and would have been around more at the time of Patrick’s arrival in December.

**Bibliography.**

Frisch, Otto R., *What Little I Remember*, Cambridge University Press 1979

Powers, Thomas, *Heisenberg’s War*, Cape 1993