nLab electromagnetism

Idea

Electromagnetism or electrodynamics is the gauge theory whose field is the electromagnetic field, see there for more details.

The corresponding quantum field theory is quantum electrodynamics.

Related concepts

• electromagnetic radiation

  • light

• Hall effect, quantum Hall effect

  spin Hall effect, quantum spin Hall effect

• topological photonics

• magnetohydrodynamics

• Dirac charge quantization

• Einstein-Maxwell theory

• Born-Infeld theory

• vector meson dominance

• quantum field theory

  • gauge theory

    • classical electrodynamics

    • electromagnetism

    • Yang-Mills theory

    • electroweak field

  • higher U(1)-gauge theory

    • B-field

    • C-field

References

Exposition of the formulation of Maxwell's equations via differential forms and the Hodge star operator:

• 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]

More advanced discussion:

• Mikio Nakahara, Section 10.5 of: Geometry, Topology and Physics, IOP 2003 (doi:10.1201/9781315275826, pdf)

Discussion of electromagnetism in the generality of quantum field theory on curved spacetimes originates with

• Jonathan Dimock, Quantized Electromagnetic Field on a Manifold, Reviews in Mathematical Physics, Volume 04, Issue 02, 1992 (doi:10.1142/S0129055X92000078)

and is further developed in (e.g. regarding Hadamard states) in

• K. Sanders, Claudio Dappiaggi, T.-P. Hack, Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss’ law, Commun. Math. Phys. 328(2), 625–667 (2014)

• Claudio Dappiaggi, D. Siemssen, Hadamard states for the vector potential on asymptotically flat spacetimes, Rev. Math. Phys. 25, 1 (2013)

• Claudio Dappiaggi, B. Lang, Quantization of Maxwell’s equations on curved backgrounds and general local covariance, Lett. Math. Phys. 101(3), 265–287 (2012)