Towards Quantum Field Theory of D-Particles

Abstract

§1. Remarks on string field theory from a historical perspective In the first part of the present written report, I would like to review the early history of string theory from the viewpoint of its connection to field theory as well as string field theory, including my personal recollections. I feel somewhat reluctantly that this may be justified, in view of the fact that among the participants of this conference I belong to the eldest generation, starting my research career four decades ago almost simultaneously with the birth of string theory. A hope is that these remarks from a personal point of view tell us something about the nature of string field theory, and also that reflections on the historical side are of some help for conveying to the reader the background and motivations for my recent singular attempt toward a ‘field theory’ of D0-branes. String theory started with the Veneziano amplitude which was originally proposed to be a mathematical model for a duality between Regge-pole and resonance behaviors, being established in the late 1960s experimentally as the characteristics of the scattering of hadrons. The Regge-pole behavior corresponds to the exchange of composite states of hadrons exchanged in t-channel, while the resonance behavior corresponds to the formation of resonating states composed of scattering hadrons in s-channel. The duality meant that a single scattering amplitude can be described either by summation over the Regge pole contributions or over the resonances, but not both simultaneously. The Veneziano formula was regarded as an ideal realization of this duality in the limit of narrow resonance approximation, ignoring finite life times of hadronic states.