Field Theories from the Relativistic Law of Motion

TL;DR

This paper derives fundamental field theories like electromagnetism and gravity from the relativistic law of motion, showing a deep connection between force laws and their corresponding field descriptions.

Contribution

It demonstrates that linear and quadratic relativistic force laws uniquely lead to gauge theories and General Relativity, respectively, based solely on dynamical properties.

Findings

Linear force law yields gauge theories such as Maxwell and Yang-Mills.

Quadratic force law leads to the tensor theory of gravity, General Relativity.

Dynamical properties of force laws determine the corresponding field theories.

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 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.