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 could be the Abelian Maxwell electrodynamics or the non-Abelian Yang-Mills theory. 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 tensor theory of gravitational field - general relativity. It is remarkable that a purely dynamical property of the force law leads uniquely to the corresponding field theories.
Publication Source (Journal or Book title)
Modern Physics Letters A
Singh, P., & Dadhich, N. (2001). Field theories from the relativistic law of motion. Modern Physics Letters A, 16 (2), 83-90. https://doi.org/10.1142/S0217732301002900