The premetric approach to electromagnetism in the 'waves are not vectors' debate

Main Article Content

A. Bossavit

Abstract

A plea for the introduction, in advanced electromagnetics courses, of some basic differential geometric notions:  covectors,  differential forms, Hodge operators.  The main advantages of this evolution should be felt in computational electromagnetism.  It may also shed some new light on the concept of material isotropy.

Downloads

Download data is not yet available.

Article Details

How to Cite
Bossavit, A. (2012). The premetric approach to electromagnetism in the ’waves are not vectors’ debate. Advanced Electromagnetics, 1(1), 97-102. https://doi.org/10.7716/aem.v1i1.66
Section
Research Articles

References


  1. W. L. Burke, Applied Differential Geometry, Cambridge University Press, Cambridge (U. K.), 1985. Th. Frankel, The Geometry of Physics, An Introduction, Cambridge U. P., Cambridge (U. K.), 1997.

  2. W. L. Burke, Manifestly parity invariant electromagnetic theory and twisted tensors, J. Math. Phys., 24: 65–69, 1983.
    View Article

  3. C. W. Misner, K. S. Thorne, and J. W. Wheeler, Gravitation, Freeman, New York, 1973.

  4. A. S. Goldhaber and W. P. Trower, Resource Letter MM-1: Magnetic monopoles, Am. J. Phys., 58: 429–439, 1990.
    View Article

  5. F. W. Hehl and Y. N. Obukhov, Electric/magnetic reciprocity in premetric electrodynamics with and without magnetic charge, and the complex electromagnetic field, Phys. Lett. A, 323: 169–175, 2004.
    View Article

  6. A. Bossavit, On the notion of anisotropy in constitutive laws: some implications of the ‘Hodge implies metric’ result, COMPEL, 20: 233–239, 2001.
    View Article

  7. A. Fresnel, Mémoire sur la double réfraction, Mémoires de l’Acad. de l’Institut de France, 7: 45–176, 1827.

  8. F. Kottler, ‘Maxwell’sche Gleichungen und Metrik, Sitzungber. Akad. WienIIa, 131: 119–146, 1922.

  9. E. J. Post, “Kottler–Cartan–van Dantzig (KCD) and Noninertial Systems”, Found. Phys., 9: 619–640, 1979.
    View Article

  10. M. J. A. Schouten and D. Van Dantzig, On ordinary quantities and W-quantities, Compositio Math., 7: 447–473, 1939.

  11. A. Bossavit, Discretization of Electromagnetic Problems: The ‘Generalized Finite Differences Approach’, in W. H. A. Schilders, E. J. W. Ter Maten (Eds): Numerical Methods in Electromagnetism (Handbook of Numerical Analysis, Vol. 13), Elsevier, Amsterdam, pp. 105–197, 2005.

  12. J. H. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell’s Equations, J. Comp. Phys., 151: 881–909, 1999.
    View Article

  13. H. Whitney, Geometric Integration Theory, Princeton U. P., Princeton, 1957.