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On Dirac's incomplete analysis of gauge transformations [An article from: Studies in History and Philosophy of Modern Physics]
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This digital document is a journal article from Studies in History and Philosophy of Modern Physics, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.
Description:
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 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.
Description:
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 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.
