Bradley, Clara
(2024)
Do First-Class Constraints Generate Gauge Transformations? A Geometric Resolution.
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Abstract
The standard definition of a gauge transformation in the constrained Hamiltonian formalism traces back to Dirac (1964): a gauge transformation is a transformation generated by an arbitrary combination of first-class constraints. On the basis of this definition, Dirac argued that one should extend the form of the Hamiltonian in order to include all of the gauge freedom. However, there have been some recent dissenters of Dirac's view. Notably, Pitts (2014) argues that a first-class constraint can generate "a bad physical change" and therefore that extending the Hamiltonian in the way suggested by Dirac is unmotivated. In this paper, I use a geometric formulation of the constrained Hamiltonian formalism to argue that there is a flaw in the reasoning used by both sides of the debate, but that correct reasoning supports the standard definition and the extension to the Hamiltonian. In doing so, I clarify two conceptually different ways of understanding gauge transformations, and I pinpoint what it would take to deny that the standard definition is correct.
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Do First-Class Constraints Generate Gauge Transformations? A Geometric Resolution. (deposited 28 Aug 2024 03:35)
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