BRST formalism of <i>f</i>(<i>R</i>) gravity

Abstract We perform the manifestly covariant quantization of f ( R ) gravity in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. We explicitly calculate various equal-time commutation relations (ETCRs), in particular the ETCR between the metric and its time derivative, and show that it has a nonvanishing and nontrivial expression, whose situation should be contrasted to the previous result in higher-derivative or quadratic gravity where the ETCR was found to be identically vanishing. We also clarify global symmetries, the physical content of f ( R ) gravity, and clearly show that this theory is manifestly unitary and has a massive scalar and massless graviton as physical modes.