The influence of Stanley Mandelstam
Michael Green · International Journal of Modern Physics A · 2017
I hardly knew Stanley Mandelstam -our paths rarely crossed, and when they did our discussions were restricted to technical, rather than personal, issues.It is, however, an honour to be asked to write this short memoir since his work was hugely innovative and he was one of the pioneers who laid the foundations for much of the subject of my research.My interests as a PhD student in Cambridge in the late 1960's were strongly influenced by the ideas of S-matrix theory that had emerged from Berkeley, largely following the work of Chew, and Mandelstam.Stanley made use of his exceptional understanding of the analytic properties of perturbative quantum field theory to motivate a more rigorous approach to Smatrix theory.This led him to the covariant formulation of scattering amplitudes in terms of "Mandelstam variables" and to the "Mandelstam representation", which provided an elegant framework for discussing dispersion relations.He was one of the early contributors to Regge pole theory and its relation to sums of Feynman diagrams.These were the basic ingredients for much of the S-matrix programme that attempted to explain the strong interactions in the absence of a quantum field theory description.Stanley was prominent in the series of developments relating to the strong interactions that grew out of the S-matrix programme and were taking place during my period as a graduate student.He realised that the dual relation between resonances and Regge poles necessitates the presence of an infinite number of narrow resonance poles lying on linear Regge trajectories.This was subsequently explicitly realised in Veneziano's 1968 paper that introduced the dual resonance model that was supposed to describe meson scattering and later developed into string theory.Stanley immediately began making seminal contributions to the development of dual models and then to their formulation as string theories.He and his Berkeley group formulated dual model n-particle tree amplitudes that included spinning external particles, as well as internal symmetries, which are closely related to the fermionic string theory of Ramond, Neveu and Schwarz.I visited Berkeley in the Summers of 1971 and 1972 but, to my regret, I did not interact with Stanley.In the Summer of 1973 I participated in a small and very interesting conference on dual models at CERN, in which the highlight was the arrival of preprints of two remarkable papers by Stanley -although he himself did not attend the meeting.These papers demonstrated how to calculate scattering amplitudes in bosonic string theory and in Ramond-Neveu-Schwarz string theory by making use of the light-cone gauge.The lightcone gauge for free string theory had been introduced in a beautiful paper by Goldstone,