Do First-Class Constraints Generate Gauge Transformations? A Geometric Perspective

Explore the intricate relationship between first-class constraints and gauge transformations in constrained Hamiltonian formalism through this thought-provoking talk by Clara Bradley from the University of California, Irvine. Delve into the standard definition of gauge transformations as proposed by Dirac and examine the criticisms raised by Pitts and Pons regarding its completeness and implications. Investigate the geometric formulation of constrained Hamiltonian formalism and its potential to motivate the extension of the Hamiltonian independently from gauge transformation considerations. Analyze the arguments presented to support the standard definition of gauge transformations while addressing the criticisms. Consider the implications of rejecting the claim that the constrained Hamiltonian formalism is fully described by the geometric picture and explore potential avenues for further investigation in this complex area of physics.