How to Choose a Gauge? The Case of Hamiltonian Electromagnetism.
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 int...
| Published in: | Erkenntnis Vol. 89; no. 4; pp. 1581 - 1616 |
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| Main Authors: | , |
| Format: | Article |
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Springer Nature
Apr2024
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| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=176583024&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 176583024 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 01650106 5KZ jtl: Erkenntnis issn: 01650106 maglogo: N pubinfo: dt: Apr2024 vid: 89 iid: 4 pid: 237 pub: Springer Nature artinfo: ui: 176583024 10.1007/s10670-022-00597-9 ppf: 1581 ppct: 35 formats: fmt: – @attributes: type: T – @attributes: type: P size: 1.7MB tig: atl: How to Choose a Gauge? The Case of Hamiltonian Electromagnetism. aug: au: Gomes, Henrique Butterfield, Jeremy affil: https://ror.org/013meh722 Trinity College, University of Cambridge, Cambridge, UK su: Helmholtz, Hermann von, 1821-1894 Electromagnetism Degrees of freedom Equations of motion Electric fields Gauge symmetries sug: subj: Helmholtz, Hermann von, 1821-1894 Electromagnetism Degrees of freedom Equations of motion Electric fields Gauge symmetries ab: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Erkenntnis is a copyright of Springer, 2024. All Rights Reserved. item: Erkenntnis holder: Springer Nature dt: @attributes: year: 2024 holdings: @attributes: islocal: N |
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