Abstract
In 1864, the Scottish physicist James Clerk Maxwell undertook the task of combining all that was then known about electric and magnetic phenomena into a single, encompassing theory. Maxwell used as a template the mathematical structure of the well-known theory of elastic media. In this regard, Maxwell followed in the long tradition of applying established mathematical tools to a new problem. Maxwell’s original papers are somewhat difficult to read because they do not incorporate the modern vector notation invented by Oliver Heaviside. In this regard, it makes Maxwell’s achievement even more compelling as he was able to understand the mathematical structure present in the equations even without the notational support that makes it more evident.
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- 1.
Hertz published “Über sehr schnelle electrische Schwingungen” in the Annalen der Physik in 1887.
- 2.
We use the symbol V for the electric potential, as is traditional and distiguish it from the volume \(\mathcal{V}\) by using a different font. Students will have to be constantly vigilant, as such subtleties can be obscured when copying equations from the chalkboard.
- 3.
The term gauge is due to Hermann Weyl, who was studying the effects of scaling transformations on Lagrangian systems.
- 4.
We’re skipping over some details of other terms that generally can be forced to vanish by assuming that the Green’s function and the source term vanish sufficiently fast at large distances.
- 5.
The operator is also known to mathematicians as a 1-form. There is a veritable ocean of mathematical literature on the extension of simple, ordered tuples (vectors) into more complex entities (tensors).
- 6.
Boussinesq published “Théorie de lintumescence liquide appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire” in the Comptes Rendus Hebdomi-naires des Séances de l’Académie des Sciences in 1871. Korteweg and de Vries published “On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves” in the Philosophical Magazine in 1895.
- 7.
Gardner et al. published “Method for solving the Korteweg-de Vries equation” in the Physical Review Letters in 1967.
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© 2018 Mark A. Cunningham
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Cunningham, M.A. (2018). On the Nature of the Photon. In: Beyond Classical Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-63160-8_2
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DOI: https://doi.org/10.1007/978-3-319-63160-8_2
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