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September 5, 2025

BRST Formalism of f(R) Gravity

Key Points

The study shows that the equal-time commutation relations in f(R) gravity yield a nontrivial expression, differing from quadratic gravity.
It explicitly calculates the ETCR between the metric and its time derivative, demonstrating unique features in f(R) gravity.
The findings clarify the global symmetries of f(R) gravity, emphasizing its physical content and implications in quantum gravity.
This theory is manifestly unitary and includes both a massive scalar and a massless graviton as physical modes.

Abstract

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 particlular, 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 the 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.

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