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How to Choose a Gauge? The case of Hamiltonian Electromagnetism

Gomes, Henrique and Butterfield, Jeremy (2022) How to Choose a Gauge? The case of Hamiltonian Electromagnetism. [Preprint]

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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 (2018) discussion, which advocated the Coulomb gauge.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Gomes, Henriquegomes.ha@gmail.com0000-0002-9285-0090
Butterfield, Jeremyjb56@cam.ac.uk0000-0002-0215-5802
Additional Information: Forthcoming in Erkenntnis. This version gives some clarifications (in Sections 1.1 and 4) about the nature of the non-locality implied by the Gauss constraint.
Keywords: gauge symmetries, constrained dynamics, ontology of physical theories, Coulomb gauge, Helmholtz decomposition
Subjects: Specific Sciences > Physics > Classical Physics
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Jeremy Butterfield
Date Deposited: 09 Jul 2022 12:18
Last Modified: 09 Jul 2022 12:18
Item ID: 20866
Subjects: Specific Sciences > Physics > Classical Physics
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Date: July 2022
URI: http://philsci-archive.pitt.edu/id/eprint/20866

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