dorsal/arxiv
View SchemaOn Dirac's incomplete analysis of gauge transformations
| Authors | Josep M. Pons |
|---|---|
| Categories | |
| ArXiv ID | physics/0409076 |
| URL | https://arxiv.org/abs/physics/0409076 |
| Journal | Stud.Hist.Philos.Mod.Phys. 36 (2005) 491-518 |
Abstract
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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"abstract": "Dirac\u0027s approach to gauge symmetries is discussed. We follow closely the\nsteps that led him from his conjecture concerning the generators of gauge\ntransformations {\\it at a given time} --to be contrasted with the common view\nof gauge transformations as maps from solutions of the equations of motion into\nother solutions-- to his decision to artificially modify the dynamics,\nsubstituting the extended Hamiltonian (including all first-class constraints)\nfor the total Hamiltonian (including only the primary first-class constraints).\nWe show in detail that Dirac\u0027s analysis was incomplete and, in completing it,\nwe prove that the fulfilment of Dirac\u0027s conjecture --in the \"non-pathological\"\ncases-- does not imply any need to modify the dynamics. We give a couple of\nsimple but significant examples.",
"arxiv_id": "physics/0409076",
"authors": [
"Josep M. Pons"
],
"categories": [
"physics.hist-ph",
"gr-qc",
"hep-th",
"math-ph",
"math.MP"
],
"journal_ref": "Stud.Hist.Philos.Mod.Phys. 36 (2005) 491-518",
"title": "On Dirac\u0027s incomplete analysis of gauge transformations",
"url": "https://arxiv.org/abs/physics/0409076"
},
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