FIELD THEORIES FROM THE RELATIVISTIC LAW OF MOTION
Parampreet SinghInter-University Centre for Astronomy & Astrophysics, Post Bag 4, Ganeshkhind, Pune 411007, IndiaNaresh DadhichInter-University Centre for Astronomy & Astrophysics, Post Bag 4, Ganeshkhind, Pune 411007, India
2001en
ABI
Abstract
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.
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