Gauge transformations for dynamical systems with first- and second-class constraints

Gauge theories with second-class constraints are investigated. The relation between primary first-class constraints and gauge degrees of freedom is shown. Next, a method to obtain the generator of the gauge transformation is presented. The generator is expressed in terms of a linear combination of constraints. In the expression, all constraints are employed without distinguishing the first- from the second-class ones. The generator consists of the generator of the pure gauge transformation and that of global symmetry transformations with constant parameters. The method to construct the generator can be applied to a system having only second-class constraints, and extended Noether currents (generators) with constant parameters are obtained. If the first-class constraints and the Hamiltonian are in involution, the generator of pure gauge transformations can be obtained using only the first-class constraints