The effects of symmetry breaking and renormalization on a unified field theory can be simulated by the use of a deformed gauge group instead of $U(3)$. Here the use of a deformation of $u(3)$ called $u_Q(3)$, with three independent parameters, is proposed and illustrated by obtaining a mass formula with electromagnetic mass splitting, as well as the hypercharge and isospin dependence, for the baryons.

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