DYNAMICAL-SYSTEMS WITH FIRST-CLASS AND 2ND-CLASS CONSTRAINTS .2. LOCAL-SYMMETRY TRANSFORMATIONS

In the framework of the generalized Hamiltonian formalism by Dirac, lo cal symmetries of dynamical systems with first- and second-class const raints are investigated. The method of constructing the generator of l ocal-symmetry transformations is presented both for theories with an a lgebra of constraints of a special form (a majority of the physically interesting theories) and in the general case without restrictions on the algebra of constraints. It is proven that second-class constraints do not contribute to the transformation law of the local symmetry ent irely stipulated by all the first-class constraints. A mechanism of th e occurrence of higher derivatives of coordinates and group parameters in the symmetry transformation law in Noether's second theorem is elu cidated. In the latter case it is shown that the obtained transformati ons of symmetry are canonical in the extended (by Ostrogradsky) phase space. It is thereby shown that in the general case the degeneracy of theories with first- and second-class constraints is due to their inva riance under local-symmetry transformations.