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Lorentz transformation of Debye potentials
1.See, for example, A. Nisbet, Proc. R. Soc. (London), Ser. A 231, 250 (1955);
1.J. Cohen and L. Kegels, Phys. Rev. D 10, 1070 (1974).
2.These points will be clarified in Sec. II of this article.
3.See, for example, J. Jackson, Classical Electrodynamics (Wiley, New York, 1962), Chap. 7.
4.These simple equations apply only to the case of no sources and no matter.
5.Under reflections the potential φ transforms as
6.Equations (5) and (6) obviously satisfy the divergence conditions (1) and (2). The wave equations arise as a result of applying Eqs. (3) and (4) to E and B.
7.In what follows all indices will be manipulated with the Lorentz metric whose signature is
8.One also needs to use the corresponding covarient transformations of the partial derivatives.
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