Abstract
We wish to determine the correct partial differential equation(s) for describing a relativistic particle. A physical foundation is presented for using a parametrized wave equation with the general form
where s is the invariant evolution parameter. Several forms have been proposed for the generator K of evolution parameter translations. Of the proposed generators, only the generator K 2 which is proportional to the inner product P μ P μ of fourmomentum operators can be derived from first principles, notably a probabilistic basis. Although experimental tests must be made to establish the validity of K 2,we conclude that K 2 is the leading theoretical candidate for the form of a generator of evolution parameter translations.
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Fanchi, J.R. Evaluating the validity of parametrized relativistic wave equations. Found Phys 24, 543–562 (1994). https://doi.org/10.1007/BF02058063
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DOI: https://doi.org/10.1007/BF02058063