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 | |||||||||
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| 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 |
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| 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 |
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| Date: | October 2022 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21277 |
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