On Dirac's incomplete analysis of gauge transformations

Details On Dirac's incomplete analysis of gauge transformations On Dirac's incomplete analysis of gauge transformations

2004-09-16

arxiv.org/abs/physics/0409076v2

Stud.Hist.Philos.Mod.Phys. 36 (2005) 491-518

Physics

History and Philosophy of Physics

36 pages. Additional references and a new paragraph in the introduction. Version to be published in Studies in History and Phi

Scientific paper

Dirac's approach to gauge symmetries is discussed. We follow closely the steps that led him from his conjecture concerning the generators of gauge transformations {\it at a given time} --to be contrasted with the common view of gauge transformations as maps from solutions of the equations of motion into other solutions-- to his decision to artificially modify the dynamics, substituting the extended Hamiltonian (including all first-class constraints) for the total Hamiltonian (including only the primary first-class constraints). We show in detail that Dirac's analysis was incomplete and, in completing it, we prove that the fulfilment of Dirac's conjecture --in the "non-pathological" cases-- does not imply any need to modify the dynamics. We give a couple of simple but significant examples.

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