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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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Electromagnetism and differential geometry

Electromagnetism and differential geometry

Chapter:
(p.383) 22 Electromagnetism and differential geometry
Source:
Relativity in Modern Physics
Author(s):

Nathalie Deruelle

Jean-Philippe Uzan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198786399.003.0040

This chapter begins by examining p-forms and the exterior product, as well as the dual of a p-form. Meanwhile, the exterior derivative is an operator, denoted d, which acts on a p-form to give a (p + 1)-form. It possesses the following defining properties: if f is a 0-form, df(t) = t f (where t is a vector of Eₙ), which coincides with the definition of differential 1-forms. Moreover, d(α‎ + β‎) = dα‎ + dβ‎, where α‎ and β‎ are forms of the same degree. Moreover, the exterior calculus can be used to obtain a compact and elegant formulation of Maxwell’s equations.

Keywords:   electromagnetism, differential geometry, p-forms, exterior product, dual of a p-form, exterior derivatives, exterior calculus, Maxwell’s equations

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