Abstract
THE outstanding difficulty in obtaining the equation of motion of a spinning particle in a meson field which will take account of the reaction of the emitted meson field and is free from singularities is well known. The equation of motion was first obtained by Heisenberg1 for a dipole of finite extension and is therefore not relativistically invariant. The relativistically invariant equations of motion for a point dipole which have been developed by Bhabha and Corben2 and by Bhabha3 are extremely complicated and involve a number of arbitrary constants which are not determined uniquely. These equations in their final form are free from singularities, and have been proved to involve only the contribution of the so-called radiation field, denned as half the retarded minus the advanced field, which is finite on the world line. However, the equations are established by proving that the singular terms are perfect differentials and can therefore be subtracted away.
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References
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MAJUMDAR, R., GUPTA, S. The Meson Field and the Equation of Motion of a Spinning Particle. Nature 161, 410–411 (1948). https://doi.org/10.1038/161410a0
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DOI: https://doi.org/10.1038/161410a0
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