Gauge generators, Dirac's conjecture, and degrees of freedom for constrained systems

Abstract

A necessary and sufficient condition for a function to be a generator of dynamical symmetry transformations in hamiltonian formalism is derived and presented in two forms, one of which involves an evolution operator connecting hamiltonian and lagrangian formalisms. As a particular case gauge transformations are studied. A careful distinction between gauge transformations of solutions of equations of motion and gauge transformations of points in phase space allows us to give a definitive clarification of the so-called Dirac conjecture (that is to say: the "ad hoc" addition of all the secondary first class constraints to the hamiltonian). Finally, the gauge fixing procedure is studied in both hamiltonian and lagrangian formalisms, and it is proven, in a nontrivial way, that the true number of degrees of freedom is the same for both formalisms. © 1988.