It is shown that a relativistic basis for invariance under $\mathrm{SU}\left(6\right)\mathrm{}$ exists only if the group structure is extended to $U^{+}\mathrm{}\left(6\right)\mathrm{}\otimes U^{-}\mathrm{}\left(6\right)\mathrm{}$ for any interaction terms. The notion of an inhomogeneous extension ${U_w}^{+}\mathrm{}\left(6\right)\mathrm{}\otimes {U_w}^{-}\mathrm{}\left(6\right)\mathrm{}$ is introduced. This extension leaves the kinetic-energy terms invariant, though it still does not provide a fully satisfactory theory.

• Received 10 December 1964

DOI:https://doi.org/10.1103/PhysRev.138.B420