Remarks on Gauge Invariance and First-Class Constraints

Understand

Gauge symmetries lead to first-class constraints.

• This assertion is of course true only for non trivial gauge symmetries, i.e., gauge symmetries that act non trivially on-shell on the dynamical variables.
• We illustrate this well-appreciated fact for time reparametrization invariance in the context of modifications of gravity -suggested in a recent proposal by Horava-in which the Hamiltonian constraint is deformed by arbitrary spatial diffeomorphism invariant terms, where some subtleties are found to arise.