Introduction

During the Fifties it became clear that quantum electrodynamics (QED), constructed by applying the quantization rules to classical electrodynamics, was in very good agreement with experimental results. In particular, QED accounted for the deviations observed in experiments with respect to the Dirac theory of electrons and positrons. This was considered a major success of field theory.

In the following years, many efforts were made in the attempt to build a suitable theory for the description of the weak and strong interactions of elementary particles. These efforts culminated in the formulation of the electro-weak theory of Weinberg and Salam in 1967, and quantum chromodynamics in 1973. These are the two fundamental blocks of the Standard Model.

In the Sixties, when the theoretical community was still seeking a satisfying theory of strong interactions, several alternative approaches were explored, to overcome the encountered difficulties. In particular, one of these, the S-matrix, complemented with the bootstrap hypothesis and Dolen–Horn–Schmid duality, was to give rise to dual models and string theory.

The aim of the present Chapter is to recall some of the relevant results which originated in this context, in the years between 1961 and 1968, and which led to the Veneziano formula. In the next Section I will sketch the SU(3) symmetry and the quark model. In Section 6.3 I will recall current algebra, with a glance at its exploitation by means of sum rules.