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    An electric charge has no screw sense—a comment on the twistfree formulation of electrodynamics by da Rocha & Rodrigues

    Itin, Yakov
    Obukhov, Yuri N.
    Hehl, F. W. (Friedrich W.), 1937-
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    [PDF] ElectricChargeHasNoScrewSense.pdf (118.7Kb)
    Date
    2010
    Format
    Article
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    Abstract
    Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the “derivation” of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.
    URI
    http://hdl.handle.net/10355/5130
    Part of
    Mathematics publications (MU)
    Citation
    Annalen der Physik, 27 January 2010
    Rights
    OpenAccess.
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
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    • Mathematics publications (MU)
    • Physics and Astronomy publications (MU)

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