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A vector product formulation of special relativity and electromagnetism

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Abstract

The vector product method developed in previous articles for space rotations and Lorentz transformations is extended to the cases of four-vectors, anti-symmetric tensors, and their transformations in Minkowski space. The electromagnetic fields are expressed in “six-vector” form using the notationH +iE, and this vector form is shown to be relativistically invariant. The wave equations of electromagnetism are derived using these vector products. The following three equations are deduced, which summarize electrodynamics in a compact form: (1) Maxwell's four equations expressed as one, (2) the scalar and vector potential wave equations combined into one relation, and (3) the wave equations for the electric and magnetic fields and the continuity equation combined together. Space inversion, time reversal, and magnetic monopoles are also treated.

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Authors and Affiliations

  1. Physics Department, University of South Carolina, Columbia, South Carolina

    Charles P. Poole Jr., Horacio A. Farach & Yakir Aharonov

Authors
  1. Charles P. Poole Jr.
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  2. Horacio A. Farach
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  3. Yakir Aharonov
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On leave of absence from the University of Tel Aviv.

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Poole, C.P., Farach, H.A. & Aharonov, Y. A vector product formulation of special relativity and electromagnetism. Found Phys 10, 531–553 (1980). https://doi.org/10.1007/BF00715038

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  • DOI: https://doi.org/10.1007/BF00715038

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