F.G. Tkebuchava

Local symmetries in systems with constraints

For arbitrary systems with first-class constraints the local gauge transformations are constructed in phase and configuration spaces, i.e. a method for obtaining symmetry transformations in the second Noethers theorem is given.

Gauge transformations in constrained theories

A method is proposed for constructing infinitesimal gauge transformations for an arbitrary degenerate Lagrangian without restrictions on the constraint algebra. It is thereby shown that in the general case degeneracy of a theory is due to its gauge invariance.

Higher derivatives in gauge transformations

A mechanism of occurrence of higher derivatives of the coordinates in the symmetry transformation law in Noethers second theorem is elucidated. It is shown that the corresponding transformations in the Hamiltonian formalism are canonical in an extended phase space.

PHASE SPACE IN SINGULAR THEORIES

The method is formulated for constructing the generators of gauge transformations in the phase space for a given singular Lagrangian. These generators are used to impose the necessary and sufficient conditions on gauge functions. The results are analyzed for particular examples.