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First-class constraints generate gauge transformations in electromagnetism (reply to Pitts)

Pooley, Oliver and Wallace, David (2022) First-class constraints generate gauge transformations in electromagnetism (reply to Pitts). [Preprint]

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Abstract

Brian Pitts has recently claimed to show via straightforward calculation that, at least in the case of Hamiltonian electromagnetism, an arbitrary first-class constraint ``generates not a gauge transformation, but a bad physical change'' (Annals of Physics 351 (2014) pp.382--406; http://philsci-archive.pitt.edu/11015/).
We show, via a straightforward calculation, that a transformation generated by an arbitrary first-class constraint relates gauge-equivalent phase space points, vindicating orthodoxy. Pitts, however, is primarily concerned with transformations of entire histories, rather than of instantaneous states. We show that, even in this context, a transformation generated by an arbitrary first-class constraint is also a gauge transformation, once the empirically observed electric field is correctly identified via its dynamical interactions with charge, and not simply given stipulatively as a certain combination of the potential and its derivatives.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Pooley, Oliveroliver.pooley@philosophy.ox.ac.uk
Wallace, Daviddavid.wallace@pitt.edu
Keywords: Gauge theory Canonical transformations Constrained Hamiltonian formalism
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Professor David Wallace
Date Deposited: 17 Oct 2022 17:05
Last Modified: 17 Oct 2022 17:05
Item ID: 21277
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Symmetries/Invariances
Date: October 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21277

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