nLab electromagnetism




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT



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.


Classical electromagnetism


  • Edmund T. Whittaker:

    A History of the Theories of Aether and Electricity

    • Vol. 1: The Classical Theories

      From the age of Descartes to the close of the Nineteenth century

      (1910, 1951) [pdf]

    • Vol. 2: The Modern Theories 1900-1926

      (1953) [pdf]

    reprinted by Humanities Press (1973)

    [Wikipedia entry]

Textbook accounts of classical electrodynamics:

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:

Phase space and Poisson brackets

For more see the references at Yang-Mills theory – References – Phase space and canonical quantization.

Quantum electromagnetism

Discussion of Fock space quantization based on careful analysis of the covariant phase space:

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

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)

Discussion of global topological effects due to flux quantization:

Last revised on February 11, 2024 at 14:10:36. See the history of this page for a list of all contributions to it.