​Roy Chisholm (1926 - 2015)

A Year at CERN (1962-63)

We left Cardiff in the summer of 1962 with children aged 3 (Carol) and 1 (David), and set off for a 5-week holiday on the Mediterranean, where we camped for the first time. Monty and Carol were ill when we arrived in Geneva, but we were fortunate in having arranged with Roger Phillips (of the Rutherford Laboratory) to take over his apartment in Annemasse for a few weeks. By asking around, I was able to rent a small chalet at Mies belonging to the remarkable Family Steffen. We stayed there happily for the rest of the year, and were most kindly and interestingly treated by the Steffens.

My early impression of CERN was that everyone was very busy at his or her own task, and it was slightly overwhelming to suddenly be at a world centre for particle physics. I finished off a piece of work started at Cardiff, showing that the (n,n) Pade approximant, formed from the power series solution of a Fredholm integral equation with kernel of rank n, was the exact solution of the equation (ref 10); it followed that the n-infinity limit gives the solution of a Fredholm equation with compact kernel.

My interest in summing divergent power series led me to discover something about 'band- wagons'. The latest theoretical fashion early in 1963 was 'peratisation', Pais's method of summing divergent series by including only the dominant term of each order. A young French theorist had been asked to give two seminars on the topic, and after the first I realised that the method was nonsensical. At the end of his second lecture I gave this 2- minute counter-example:

The nth term of the series to be summed is the sum of the nth powers of X and Y, where X is almost unity, and Y is large. The peratisation rule eliminates the powers of X, but the dominant term in the sum is in fact 1/(1-X), the sum of these powers.

I wrote the series on the board. Not only was there no response from the audience, but many of them had their eyes half-closed and glazed over, as though they did not really want to see what I had written. Work continued on the subject for several months after these seminars.

My interest in Feynman graph computations was revived by meeting Dr Mike Levine, who was an expert programmer. In the summer of 1963, we started to calculate the sixth-order contribution to the magnetic moment of the electron. Sadly, we both left CERN after a few months. I went to a very difficult and onerous job in Dublin; Mike went on a 3-year Fellowship at La Jolla. With very little help from me, he struggled on for a further year with the calculation, but gave up on the advice of Professor Norman Kroll, who told him to do something simpler in order to get some publications - 'publish or perish' is not new. However, my interest was revived in algorithms for scalar products of Dirac gamma-algebra, and I completed the set of three basic algorithms (ref 11); although the first two were independently discovered by Caianello and Fubini, my name has been attached to the full set. I also began working out similar formulae for scalar products of Pauli matrices, but these were not completed for a few years (ref 12). Mike Levine eventually re-started the sixth-order moment calculation with Jon Wright, and they successfully completed it about eight years later; Kinoshita carried out the same calculation independently.

The seminars and discussions at CERN were very helpful to me, and, later, I shall tell a strange story involving a seminar given by Cabibbo. I enjoyed many hours in what John Bell called discussions, but really, I was just listening to John arguing things out for himself: this was the time when he was working out what was wrong with von Neumann's logic of measurement, and his arguments - often, it seems, starting with 'consider the harmonic oscillator' - were very educational for me. Around Easter 1963, John put his head round my door and asked 'do you want to stay another year?' I felt that it would be unfair to Trinity College to ask for a second year of leave of absence, which might well have been refused, so I declined the invitation with great reluctance. Another parallel universe!

Our two young children were involved in an incident over a CERN preprint. As a preliminary, I must explain that, before we set off for Switzerland, my son had injudiciously put his finger through the wire netting of a rabbit's cage in a pet shop, resulting in a lot of blood and screams. At CERN, old preprints were available as scrap paper, and my daughter Carol, just 4 years old, became fascinated by Feynman diagrams; I explained that they represented the tracks of fundamental particles, and she used to work hard copying them. My former supervisor Jim Hamilton visited soon after we settled in Mies. As we talked, he happened to look over Carol's shoulder, finding her hard at work on a paper by Amati, Fubini and Stanghellini on the Multiperipheral Model, which contained many elaborate Feynman graphs. He was so surprised that he took his pipe out of his mouth; he asked Carol what she was doing. 'I'm drawing Feynman diagrams', she replied enthusiastically. 'Do you like Feynman diagrams?', asked Jim. 'Yes, I like them very much.' My son David, not quite two years old, was standing nearby, so Jim asked him very kindly, 'And do you like Feynman diagrams, David?'. David, clearly aggrieved, replied firmly,'No. When I was a little boy, I was bitten by a Feynman diagram.'