2004/09/30 by Josep M. Pons · 1 citation
Physics and Astronomy · Mathematics · #physics.hist-ph #gr-qc #hep-th #math-ph #math.MP
published as Stud.Hist.Philos.Mod.Phys. 36 (2005) 491-518 · 36 pages. Additional references and a new paragraph in the introduction. Version to be published in Studies in History and Philosophy of Modern Physics
arxiv created 2005/06/02 · arxiv updated 2009/12/01
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.