Derivative-dependent metric transformation and physical degrees of freedom

Understand

We study metric transformations which depend on a scalar field $\phi$ and its first derivatives and confirm that the number of physical degrees of freedom does not change under such transformations, as long as they are not singular.

• We perform a Hamiltonian analysis of a simple model in the gauge $\phi = t$.
• In addition, we explicitly show that the transformation and the gauge fixing do commute in transforming the action.
• We then extend the analysis to more general gravitational theories and transformations in general gauges.