Deformed Wong particles

By generalizing the Feynman proof of the Lorentz force law, recently reported by Dyson, we derive equations of motion for particles possessing internal degrees of freedom ${I}^{a}$ which do not, in general, generate a finite algebra. We obtain consistency criteria for fields which interact with such particles. We use the results to argue that SU(2) gauge invariance is broken to U(1) when a particle with internal $\mathrm{S}{\mathrm{U}}_{q}(2)$ degrees of freedom is coupled to SU(2) gauge fields. We further claim that when such an $\mathrm{S}{\mathrm{U}}_{q}(2)$ particle acts as a source for the field theory, the second-rank antisymmetric field tensor, in general, cannot be globally defined.