Field theories from the relativistic law of motion

From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in four-velocity of the particle. The linear law leads to the vector gauge theory which cou ld be the Abelian Maxwell electrodynamics or the non-Abelian Yang-Mills the ory. On the other hand, the quadratic law demands space-time metric as its potential which is equivalent to demanding the principle of equivalence. It leads to the tenser theory of gravitational field - general relativity. It is remarkable that a purely dynamical property of the force law leads uniq uely to the corresponding field theories.