Abstract

We cast the flat space theory of a scalar field in generally covariant form by introducing an auxiliary field $\lambda$. The resulting theory is couched in terms of an action integral $S$, and all the fields (the scalar, the spacetime metric, and $\lambda$) are dynamical in the sense of being varied freely in $S$. Conservation of energy-momentum emerges as a formal consequence of diffeomorphism invariance, in close analogy with the situation in ordinary general relativity.