Main Article Content
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.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- 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.
- W. L. Burke, Manifestly parity invariant electromagnetic theory and twisted tensors, J. Math. Phys., 24: 65–69, 1983.
- C. W. Misner, K. S. Thorne, and J. W. Wheeler, Gravitation, Freeman, New York, 1973.
- A. S. Goldhaber and W. P. Trower, Resource Letter MM-1: Magnetic monopoles, Am. J. Phys., 58: 429–439, 1990.
- 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.
- A. Bossavit, On the notion of anisotropy in constitutive laws: some implications of the ‘Hodge implies metric’ result, COMPEL, 20: 233–239, 2001.
- A. Fresnel, Mémoire sur la double réfraction, Mémoires de l’Acad. de l’Institut de France, 7: 45–176, 1827.
- F. Kottler, ‘Maxwell’sche Gleichungen und Metrik, Sitzungber. Akad. WienIIa, 131: 119–146, 1922.
- E. J. Post, “Kottler–Cartan–van Dantzig (KCD) and Noninertial Systems”, Found. Phys., 9: 619–640, 1979.
- M. J. A. Schouten and D. Van Dantzig, On ordinary quantities and W-quantities, Compositio Math., 7: 447–473, 1939.
- 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.
- J. H. Hyman and M. Shashkov, Mimetic Discretizations for Maxwell’s Equations, J. Comp. Phys., 151: 881–909, 1999.
- H. Whitney, Geometric Integration Theory, Princeton U. P., Princeton, 1957.