Journal article
How to choose a gauge? The case of Hamiltonian electromagnetism
- Abstract:
- We develop some ideas about gauge symmetry in the context of Maxwell’s theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a decomposition of one side into subsets can be translated into a decomposition of the other. In the case of electromagnetism, this enables us to pair degrees of freedom of the electric field with degrees of freedom of the vector potential. Another benefit is that the formalism algorithmically identifies subsets of the equations of motion that represent time-dependent symmetries. For electromagnetism, these two benefits allow us to define gauge-fixing in parallel to special decompositions of the electric field. More specifically, we apply the Helmholtz decomposition theorem to split the electric field into its Coulombic and radiative parts, and show how this gives a special role to the Coulomb gauge (i.e. div(A)=0). We relate this argument to Maudlin’s (Entropy, 2018. https://doi.org/10.3390/e20060465) discussion, which advocated the Coulomb gauge.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.7MB, Terms of use)
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- Publisher copy:
- 10.1007/s10670-022-00597-9
Authors
- Publisher:
- Springer
- Journal:
- Erkenntnis More from this journal
- Volume:
- 89
- Issue:
- 4
- Pages:
- 1581-1615
- Publication date:
- 2022-08-02
- Acceptance date:
- 2022-06-14
- DOI:
- EISSN:
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1572-8420
- ISSN:
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0165-0106
- Language:
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English
- Pubs id:
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1506027
- Local pid:
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pubs:1506027
- Deposit date:
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2023-08-08
Terms of use
- Copyright holder:
- Gomes and Butterfeld
- Copyright date:
- 2022
- Rights statement:
- © The Author(s) 2022. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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