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On Dirac's incomplete analysis of gauge transformations

Pons, Josep M (2005) On Dirac's incomplete analysis of gauge transformations. Studies in History and Philosophy of Modern Physcis, 36. pp. 491-518.

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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 onstraints) 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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Item Type: Published Article or Volume
Pons, Josep
Keywords: gauge theories, gauge transformations, Dirac-Bergmann theory, constrained systems, Dirac conjecture
Depositing User: Dr josep pons
Date Deposited: 19 Mar 2016 01:50
Last Modified: 19 Mar 2016 01:50
Item ID: 11973
Journal or Publication Title: Studies in History and Philosophy of Modern Physcis
Publisher: Elsevier
DOI or Unique Handle:
Date: 2005
Page Range: pp. 491-518
Volume: 36

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