RIGID AND GAUGE NOETHER SYMMETRIES FOR CONSTRAINED SYSTEMS

摘要: We develop the general theory of Noether symmetries for constrained systems, that is, systems are described by singular Lagrangians. In our derivation, Dirac bracket structure with respect to primary constraints appears naturally and plays an important role in characterization conserved quantities associated these symmetries. The issue projectability from tangent space phase is fully analyzed, we give a geometrical interpretation conditions terms relation between quantity presymplectic form defined on it. also examine enlarged formalism results taking Lagrange multipliers as new dynamical variables; find equation characterizes this formalism, prove standard formulation particular case one. algebra generators discussed both Hamiltonian Lagrangian formalisms. frequent source appearance open algebras fact transformations momenta only coincide shell. Our apply no distinction rigid gauge symmetries; latter proof existence theories first second class do not exhibit tertiary stabilization algorithm. Among some examples illustrate results, study Abelian Chern–Simons 2n+1 dimensions. An interesting feature example its can be identified after determination secondary constraint. worked out retaining all original set variables.