The Mass Variation with Velocity in Bopp's Unitary Field Theory, I
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In the case of free motion of constant velocity, the total energy and total momentum of self-field produced by a point particle was calculated starting from energy-momentum tensor derived by Bopp and Heisenberg for the Bopp-type non-local field theory. The correct velocity variation of energy and momentum required by relativistic mechanics is not guaranteed from the beginning for the above energy-momentum tensor. From the detailed calculations in this paper, however, the correct variation upon velocity is attainable if the characteristic function ε(x) satisfies a certain condition. As this condition is very flexible, there remain possibilities of the presence of some appropriate form of ε(x) which guarantees the finiteness of the self energy of a point particle and the correct velocity variation of energy and momentum of the self-field. The examination of the energy-momentum tensor itself causes some doubt about the correctness of the energy-momentum tensor derived by Bopp and Heisenberg.
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