nLab dielectric medium

Idea

(…)

Related entries

• electromagnetism

• pre-metric electromagnetism

References

General

See most references on electromagnetism, e.g. the article

• G. Russakoff, A Derivation of the Macroscopic Maxwell Equations, American Journal of Physics 38 (1970) 1188–1195 [doi:10.1119/1.1976000]

• O. L. de Lange, R. E. Raab Surprises in the multipole description of macroscopic electrodynamics, American Journal of Physics 74 (2006) 301–312 [doi:10.1119/1.2151213]

or these textbook accounts:

• Lev Landau, Evgeny Lifshitz, Chapter II of: Electrodynamics of Continuous Media, volume 8 of: Course of Theoretical Physics, Pergamon Press (1960, 1984) [ISBN:9780750626347, archive, pdf]

• Sophocles J. Orfanidis, Section 1 of: Electromagnetic Waves and Antennas (1999-2016) [web, pdf]

• Walter Greiner, Part II of: Classical Electrodynamics, Springer (1998) [doi:10.1007/978-1-4612-0587-6]

See also

• Wikipedia, Dielectric

The “constitutive equations” are referred to as the “material-affinor” in:

• David van Dantzig, p. 426 of: The fundamental equations of electromagnetism, independent of metrical geometry, Mathematical Proceedings of the Cambridge Philosophical Society 30 4 (1934) 421-427 [doi:10.1017/S0305004100012664]

The actual terminology “constitutive relation” appears in

• Friedrich Kottler, Maxwell’sche Gleichungen und Metrik, Sitz. Akad. Wien IIa 131 (1922) 119-146 [Engl. transl. by Delphenich: pdf, pdf]

and constitutive map in:

• E. Jan Post, The constitutive map and some of its ramifications, Annals of Physics 71 2 (1972) 497-518 [doi:10.1016/0003-4916(72)90129-7]

Maxwell’s equations via differential forms

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_0$]$

  (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) $[$pdf, JSTOR$]$

• 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, §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 $[$arXiv:2009.10356, doi:10.1119/10.0001754$]$