The Ostrogradsky Method for Local Symmetries. Constrained Theories with Higher Derivatives

In the generalized Hamiltonian formalism by Dirac, the method of constructing the generator of local-symmetry transformations for systems with first- and second-class constraints (without restrictions on the algebra of constraints) is obtained from the requirement for them to map the solutions of the Hamiltonian equations of motion into the solutions of the same equations. It is proved that second-class constraints do not contribute to the transformation law of the local symmetry entirely stipulated by all the first-class constraints (and only by them). A mechanism of occurrence of higher derivatives of coordinates and group parameters in the symmetry transformation law in the Noether second theorem is elucidated. It is shown that the obtained transformations of symmetry are canonical in the extended (by Ostrogradsky) phase space. An application of the method in theories with higher derivatives is demonstrated with an example of the spinor Christ -- Lee model.Comment: 8 pages, LaTex; Talk given at the II International Workshop ``Classical and Quantum Integrable Systems'', Dubna, July 8-12, 1996; the essentially reduced version of the talk is published in Intern. J. Mod. Phys. A12, (1997)

Constrained Dynamical Systems: Separation of Constraints into First and Second Classes

In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are presented with the help of passing to an equivalent canonical set of constraints. The general structure of second-class constraints is clarified.Comment: 12 pages, LaTex; Preprint of Joint Institute for Nuclear Research E2-96-227, Dubna, 1996; to be published in Physical Review

Constrained dynamical systems: separation of constraints into first and second classes

In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are presented with the help of passing to an equivalent canonical set of constraints. The general structure of second-class constraints is clarified