The algebraic formalism of chiral $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ recently constructed by Weinberg is applied to the spectrum of nonstrange mesons. A mass formula valid under general conditions is derived. It is shown that some semiquantitative features of the formalism are in good agreement, both with existing data, and with current ideas about mass spectra such as rising Regge trajectories, meson towers, and the Veneziano representation. An attempt to fit known mesons into a coherent supermultiplet structure is described. Some arguments are given as to why this will probably not be possible without further assumptions. It is argued that if the theory is to be useful, it must be cast into a stronger form in which $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ is an approximate symmetry of the spectrum.

• Received 18 June 1969

DOI:https://doi.org/10.1103/PhysRev.186.1529