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BRST Formalism of $f(R)$ Gravity

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arxiv 2410.20270 v1 pith:QI4DHBJ2 submitted 2024-10-26 hep-th gr-qc

Ichiro Oda This is my paper · ORCID
classification hep-thgr-qc
keywords gravityconditionetcrgaugemanifestlyphysicalbrstcalculate
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Vanishing Metric Commutation Relation and Higher-derivative De Donder Gauge in Quadratic Gravity

    hep-th 2025-07 conditional novelty 6.0 of 10

    Quadratic gravity has vanishing equal-time metric commutators in both the standard and higher-derivative de Donder gauges, making the metric look classical.

  2. Conformal symmetry, SM and Gravity

    hep-th 2026-07 conditional novelty 5.0 of 10

    A Weyl-invariant SM+mirror-dark-matter+gravity model is developed via algebraic renormalization; its conformal cohomology is claimed trivial, and the required counterterms could — the author concedes not conclusively ...

  3. Anomaly footprints in SM+Gravity

    hep-th 2025-10 conditional novelty 4.0 of 10

    A mirror right-handed copy of the standard model, sharing only gravity and SU(2), is claimed to be anomaly-free, proposed as dark matter, and wrapped in a Weyl-invariant early-universe solution.

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