Field theories from the relativistic law of motion

Abstract

From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-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 spacetime metric as its potential which is equivalent to de- manding 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 correspond- ing field theories