COMMENT ON LAGRANGIANS AND SYMMETRIES

We point out that once the action is given one can derive from it the guage symmetries. Upon passing to the quantum theory, different forms of writing the gauge symmetries lead to the same results. The use of BRST techniques requires to properly include ghosts of ghosts when necessary. The gauge theory with zero lagrangian is discussed as an application. That lagrangian can be thought of, for example, as a function of the metric of a two-dimensional spacetime. The resulting "two-dimensional gravity" is shown to be quantum-mechanically consistent even if the standard description of the gauge symmetries (diffeomorphisms plus Weyl rescalings) is used. © 1990.