Journal article icon

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

Actions


Access Document


Files:
Publisher copy:
10.1007/s10670-022-00597-9

Authors


More by this author
Institution:
University of Oxford
Oxford college:
Oriel College
Role:
Author
More by this author
Role:
Author
ORCID:
0000-0002-0215-5802


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:
1572-8420
ISSN:
0165-0106


Language:
English
Pubs id:
1506027
Local pid:
pubs:1506027
Deposit date:
2023-08-08

Terms of use



Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP