On Dirac's incomplete analysis of gauge transformations
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.
Cite
@article{arxiv.physics/0409076,
title = {On Dirac's incomplete analysis of gauge transformations},
author = {Josep M. Pons},
journal= {arXiv preprint arXiv:physics/0409076},
year = {2007}
}
Comments
36 pages. Additional references and a new paragraph in the introduction. Version to be published in Studies in History and Philosophy of Modern Physics