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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
2022
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| _version_ | 1797110930891341824 |
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| author | Gomes, H Butterfield, J |
| author_facet | Gomes, H Butterfield, J |
| author_sort | Gomes, H |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T08:01:35Z |
| format | Journal article |
| id | oxford-uuid:1af6d9ab-3c62-49f9-927a-1b4674ddb5e1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:01:35Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:1af6d9ab-3c62-49f9-927a-1b4674ddb5e12023-10-09T17:21:34ZHow to choose a gauge? The case of Hamiltonian electromagnetismJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1af6d9ab-3c62-49f9-927a-1b4674ddb5e1EnglishSymplectic ElementsSpringer2022Gomes, HButterfield, JWe 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. |
| spellingShingle | Gomes, H Butterfield, J How to choose a gauge? The case of Hamiltonian electromagnetism |
| title | How to choose a gauge? The case of Hamiltonian electromagnetism |
| title_full | How to choose a gauge? The case of Hamiltonian electromagnetism |
| title_fullStr | How to choose a gauge? The case of Hamiltonian electromagnetism |
| title_full_unstemmed | How to choose a gauge? The case of Hamiltonian electromagnetism |
| title_short | How to choose a gauge? The case of Hamiltonian electromagnetism |
| title_sort | how to choose a gauge the case of hamiltonian electromagnetism |
| work_keys_str_mv | AT gomesh howtochooseagaugethecaseofhamiltonianelectromagnetism AT butterfieldj howtochooseagaugethecaseofhamiltonianelectromagnetism |