​Roy Chisholm (1926 - 2015)

Research student in Cambridge (1948-51)

In the autumn of 1948, after taking Parts 2 and 3 of the Mathematical Tripos at Cambridge, I began research into Quantum Field Theory of Elementary Particles under the supervision of Dr Nick Kemmer. The students in the group included Paul Matthews, Richard Eden, Gordon Moorhouse, Behram Kursunoglu, Angas Hurst, and from 1949, Sam Edwards and Abdus Salam. The senior academic in the group was Professor Paul Dirac, and we heard his first talk on his 1948 paper on monopoles. Several times each year, we had a seminar from one or more of Fred Hoyle, Hermann Bondi and Tom Gold; this was the age when they were hotly debating the Steady State model, and there were interesting occasions when all three were at the blackboard, arguing. 

About three weeks into my first term, Nick Kemmer handed me preprints of the first two papers by Freeman Dyson on the 'new quantum field theory', saying that they 'seemed quite interesting'. The work of Feynman, Schwinger and Tomonaga did not reach Cambridge for several months, so Dyson's papers were the first information we had about this revolution. I was given the task of explaining the first paper in a seminar 3 weeks later, and the second paper in the following week. Naturally, I did not understand the papers when I reported on them. However, this was the beginning of years of work by the group in understanding and developing the new theory.  

My first research in Cambridge extended the concept of Feynman graphs to a large thin shell in a space with signature (1,4), with periodic boundary conditions, and I calculated the generalisation of the Kaluza-Klein formula in this shell. In the limit of thinness, this reduced to the standard formula. In a seminar I gave on this result in autumn 1949, my new supervisor, Jim Hamilton, heavily criticised me on minor technical grounds. As a result of this discouragement, this original work was never published, and it was nearly 30 years before I returned to higher-dimensional theories.  

In 1950, I began a calculation of the mesonic equivalent of Karplus and Kroll's fourth order calculation of the electron's magnetic moment. I was able to systematise an operator factorisation that they had introduced, and by discovering the 'symmetric integration' formula, I showed how the energy-momentum integration could be performed automatically for any Feynman graph. A brief account of this work was published as a letter (ref 1): on the advice of Jim Hamilton, the full account (ref 2) was buried in the Cambridge Philosophical Society proceedings. The symmetric integration method was re-discovered by Nakanishi several years later, but he kindly gave me priority in his book. The method was also one of the approaches to the analysis of Feynman matrix elements in the book by Eden, Landshoff, Olive and Polkinghorne. This work formed the basis of my doctoral thesis Calculation of S-Matrix elements and Magnetic Moments (Cambridge University, 1952); in this thesis, I also derived the first set of algorithms for the reduction of scalar products of Dirac Gamma-matrices. These two algorithms were discovered independently by Caianello and Fubini. I published them later (ref 10), when I had completed the full set of algorithms.