General Relativity and Quantum Cosmology
[Submitted on 17 Oct 2022]
Title:First-class constraints generate gauge transformations in electromagnetism (reply to Pitts)
View PDFAbstract: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; arXiv:1310.2756). 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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