2001 (IPP)

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Field theories from the relativistic law of motion
(2001-06-02) Singh, Parampreet; Dadhich, Naresh
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