  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.
It is argued that when a particle with internal $SU_q(2)$ degrees of freedom is
coupled to $SU(2)$ gauge fields, $SU(2)$ gauge invariance is broken to $U(1)$.
We further claim that when such an $SU_q(2)$ particle acts as a source for the
field theory, the second rank antisymmetric field tensor, in general, cannot be
globally defined.
