Admissible gauges for constrained systems

Gauge-fixing and gaugeless methods for reducing the phase space in generalized Hamiltonian dynamics are compared with the aim to define the class of admissible gauges. In the gaugeless approach, the reduced phase space of a Hamiltonian system with first class constraints is constructed locally, without any gauge fixing, using the following procedure: Abelianization of constraints with a subsequent canonical transformation so that some of the new momenta are equal to the new Abelian constraints. As a result, the corresponding conjugate coordinates are ignorable (nonphysical) while the remaining canonical pairs correspond to the true dynamical variables. This representation of the phase space prompts the definition of the subclass of admissible gauges, canonical gauges, as functions depending only on the ignorable coordinates. A practical method to determine the canonical gauge is proposed. © 1996 The American Physical Society.