The standard definition of a gauge transformation in the constrained Hamiltonian formalism traces back to Dirac: a gauge transformation is a transformation generated by the first-class constraints. On the basis of this definition, Dirac argued that one should extend the form of the Hamiltonian in order to include all of the gauge freedom. However, Pitts (2014) argues that in some cases, a first-class constraint does not generate a gauge transformation, but rather “a bad physical change.” Similarly, Pons (2005) argues that Dirac's analysis of gauge transformations is “incomplete“ and does not provide an account of the symmetries between solutions. Both authors conclude that extending the Hamiltonian in the way suggested by Dirac is unmotivated. If correct, these arguments could have implications for other issues in the foundations of the constrained Hamiltonian formalism, including the Problem of Time. In this talk, I use a geometric formulation of the constrained Hamiltonian formalism to show that one can motivate the extension to the Hamiltonian independently from consideration of the gauge transformations, and I argue that this supports the standard definition of a gauge transformation without falling prey to the criticisms of Pitts (2014) and Pons (2005). Therefore, in order to maintain that first-class constraints do not generate gauge transformations, one must reject the claim that the constrained Hamiltonian formalism is fully described by the geometric picture; I suggest two avenues for doing so.
• The Foundations of Physics @Harvard series is co-sponsored by the Department of Philosophy
• This is a free Zoom event (no registration fee)
• The meeting ID and password will be shared with those who register
• Each talk will be 1 hour, followed by a 5-minute break and then 55 minutes for questions
• You can find more events in this series on the Foundations of Physics @Harvard website
• You can visit the YouTube channel here
Questions or comments: Jacob Barandes, <lastname>(at)g.harvard.edu (organizer)
LOCATION:Zoom STATUS:CONFIRMED DTSTART:20221101T170000Z DTEND:20221101T190000Z END:VEVENT END:VCALENDAR