Abstract
ABOUT twenty-five years ago, W. Gordon1, O. Klein2 and I3 shared in establishing a consistent set of field equations for a charge scalar ψ and the electromagnetic 4-potential Ak. To disencumber the formulæ, we take c = 1 and take the Ak to mean the ordinary potentials multiplied by 2πe/h. Then the real Lagrangian density we used reads: with The asterisk means the complex conjugate, a comma ordinary differentiation, underlining the subsequent raising of the subscript; the metric is (− 1, − 1, − 1, 1); m is the reciprocal Compton wave-length of ‘the particle’; ψ and Ak have the dimension reciprocal length; the allotment of indices is the customary (F14 = Ex etc.), as opposed to the rational. From (1) and (2) one obtains the Euler equations: with the 4-current for which the equation of continuity follows from (4) and independently from (3).
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References
Gordon, W., Z. Phys., 40, 117 (1926).
Klein, O., Z. Phys., 37, 895 (1926).
Schrödinger, E., Ann. der Phys., (4), 81 (1926); 82 (1927).
Dirac, P. A. M., Proc. Roy. Soc., A, 209, 291 (1951).
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SCHRÖDINGER, E. Dirac's New Electrodynamics. Nature 169, 538 (1952). https://doi.org/10.1038/169538a0
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DOI: https://doi.org/10.1038/169538a0
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