On the expression of classical electromagnetism, and especially of Maxwell's equations, in terms of differential forms, the de Rham differential and Hodge star operators:
Élie Cartan, §80 in: Sur les variétés à connexion affine, et la théorie de la relativité généralisée (première partie) (Suite), Annales scientifiques de l’É.N.S. 3e série, tome 41 (1924) 1-25 [numdam:ASENS_1924_3_41__1_]
(already in pregeometric form)
Charles Misner, Kip Thorne, John Wheeler, §3.4 and §4.3 in: Gravitation, W. H. Freeman, San Francisco (1973) [ISBN:9780716703440]
Theodore Frankel, Maxwell’s equations, The American Mathematical Monthly 81 4 (1974) [doi:10.1080/00029890.1974.11993557, jstor:2318995, doi:10.2307/2318995]
Walter Thirring, vol 2 §1.3 in: A Course in Mathematical Physics – 1 Classical Dynamical Systems and 2 Classical Field Theory, Springer (1978, 1992) [doi:10.1007/978-1-4684-0517-0]
Theodore Frankel, §§9-10 in: Gravitational Curvature, Freeman, San Francisco (1979) [ark:13960/t58d7nn19]
Dominic G. B. Edelen, §9.2 in: Applied exterior calculus, Wiley (1985) [GoogleBooks]
Theodore Frankel, §3.5 & §7.2b in: The Geometry of Physics - An Introduction, Cambridge University Press (1997, 2004, 2012) [doi:10.1017/CBO9781139061377]
Gregory L. Naber, §2.2 in: Topology, Geometry and Gauge fields – Interactions, Applied Mathematical Sciences 141 (2011) [doi:10.1007/978-1-4419-7895-0]
Masao Kitano, Reformulation of Electromagnetism with Differential Forms, Chapter 2 in: Trends in Electromagnetism – From fundamentals to applications, InTech (2012) 21-44 [ISBN:978-953-51-0267-0, pdf]
Sébastien Fumeron, Bertrand Berche, Fernando Moraes, Improving student understanding of electrodynamics: the case for differential forms, American Journal of Physics 88 (2020) 1083 [doi:10.1119/10.0001754, arXiv:2009.10356]
Last revised on September 25, 2024 at 09:07:30. See the history of this page for a list of all contributions to it.