Lorentz Invariance and the Interpretation ofSU(6)Theory

Abstract

Conclusions drawn so far from the $\mathrm{SU}\left(6\right)\mathrm{}$ theory are reviewed. A further discussion of the magnetic moments of long-lived baryons appears to render implausible the existence of an integrally charged sextet [$\mathrm{SU}\left(3\right)\mathrm{}$ triplet with spin ½]. The question of Lorentz invariance is discussed in some detail. A "relativistic completion" procedure is developed by means of which one can implement the requirements both of Lorentz invariance and of $\mathrm{SU}\left(6\right)\mathrm{}$ invariance for effective $S$-matrix elements. This procedure applies equally well to an interaction Lagrangian but not to the full Lagrangian including the free-field terms. The group $\mathrm{SU}\left(6\right)\mathrm{}$ apparently has to be interpreted as a dynamical group which applies to one-particle states at zero momentum. Lorentz invariance provides a natural mechanism for the first-stage breakdown of $\mathrm{SU}\left(6\right)\mathrm{}$. Considering $\mathrm{SU}\left(6\right)\mathrm{}$ invariance as a strictly zero-momentum property, we arrive nevertheless at unique predictions to order $\frac{v}{c}$ in virtue of Lorentz invariance. Baryon recoil will be treated in future papers.