Dynamics of gauge systems and Dirac's conjecture

Abstract

For systems possessing only first-class constraints, we rigorously prove that the secondary constraints act as independent generators of gauge transformations (Dirac's conjecture). The proof essentially consists in demonstrating that the total and the extended Hamiltonian generate the same time evolution for the canonical realization, f(q,p), of the gauge-invariant quantities. We also discuss the alternative realization of these quantities.