History of String Theory - 1958-1968: Regge Theory and Bootstrap Models

1958-1968: Regge Theory and Bootstrap Models

At this time, many strongly interacting particles of ever higher spins were discovered, and it became clear that they were not all fundamental. While Japanese physicist Sakata proposed that the particles could be understood as bound states of just three of them--- the proton, the neutron and the Lambda (see Sakata model), Chew believed that none of these particles are fundamental. Sakata's approach was reworked in the 1960s into the quark model by Murray Gell-Mann and George Zweig by making the charges of the hypothetical constituents fractional and rejecting the idea that they were observed particles. Chew's approach was then considered more mainstream because it did not introduce fractional charges and because it only focused on the experimentally measurable S-matrix elements, not on hypothetical pointlike constituents.

In 1958 Tullio Regge, a young theorist in Italy discovered that bound states in quantum mechanics can be organized into families with different angular momentum called Regge trajectories. This idea was generalized to relativistic quantum mechanics by Mandelstam, Vladimir Gribov and Marcel Froissart, using a mathematical method discovered decades earlier by Arnold Sommerfeld and Kenneth Marshall Watson.

Geoffrey Chew and Steven Frautschi recognized that the mesons made Regge trajectories in straight lines, which implied, via Regge theory, that the scattering of these particles would have very strange behavior—it should fall off exponentially quickly at large angles. With this realization, theorists hoped to construct a theory of composite particles on Regge trajectories, whose scattering amplitudes had the asymptotic form demanded by Regge theory. Since the interactions fall off fast at large angles, the scattering theory would have to be somewhat holistic: Scattering off a pointlike constituent leads to large angular deviations at high energies.