The analogue model for string amplitudes
D. B. Fairlie · Cambridge University Press eBooks · 2012
The beginnings I started research in the year 1957, at the time when aspiring particle physicists were being channelled into the arid field of dispersion relations, and field theory was out of fashion. I did not find the methods of analysis employed in trying to extract information out of dispersion relations to my taste. The only tool available was the analyticity of the S -matrix, as constrained by the requirements of causality, that there should be no output before input. To give an instance of the attitude to mathematics at the time, we graduate students were advised that the only pure mathematical courses worth attending were those on functional analysis, or the theory of several complex variables! The philosophy of logical positivism reigned supreme, in which one was not allowed to talk about the unobservable features of particle interactions, but only about properties of asymptotic states. This was one of the features which inhibited the invention of the concept of quarks. I had been impressed by the tractability of electrodynamics and quantum mechanics as an undergraduate, and what Wigner has called ‘The unreasonable effectiveness of Mathematics in the Natural Sciences’. In the middle of year 1968 I was feeling very pessimistic about the possibility of theorists ever being able to say anything about scattering amplitudes for hadrons, beyond the simple tree and Regge pole approximations, and was contemplating changing fields.