Quantum Scale Invariant Gravity with de Donder Gauge

Abstract

We perform the manifestly covariant quantization of a scale invariant gravity with a scalar field, which is equivalent to the well-known Brans-Dicke gravity via a field redefinition of the scalar field, in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. First, without specifying the expression of a gravitational theory, we write down various equal-time (anti-)commutation relations (ETCRs), in particular, those involving the Nakanishi-Lautrup field, the FP ghost, and the FP antighost only on the basis of the de Donder gauge condition. It is shown that choral symmetry, which is a Poincar$\acute{\mathrm{e}}$-like $IOSp(8|8)$ supersymmetry, can be derived from such a general action with the de Donder gauge. Next, taking the scale invariant gravity with a scalar field as a classical theory, we derive the ETCRs for the gravitational sector involving the metric tensor and scalar fields. Moreover, we account for how scale symmetry is spontaneously broken in quantum gravity, thereby showing that the dilaton is a massless Nambu-Goldstone particle.

arXiv comment26 pages

References in corpus (17)

• Quantum scale invariance, cosmological constant and hierarchy problem
• The Renormalization Group and Weyl-invariance
• Fake Conformal Symmetry in Conformal Cosmological Models
• Manifestly scale-invariant regularization and quantum effective operators
• Running couplings with a vanishing scale anomaly
• Restricted Weyl invariance in four-dimensional curved spacetime
• Quantum scale-invariant models as effective field theories
• Axion Homeopathy: Screening Dilaton Interactions
• Fake Conformal Symmetry in Unimodular Gravity
• Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance
• Critical gravity from four dimensional scale invariant gravity
• Planck and Electroweak Scales Emerging from Conformal Gravity
• On Restricted Weyl Symmetry
• Quadratic Gravity and Restricted Weyl Symmetry
• Higgs Potential from Weyl Conformal Gravity
• Planck scale from broken local conformal invariance in Weyl geometry
• Scale Invariance and Dilaton Mass

Cited by in corpus (3)

• BRST Formalism of Weyl Conformal Gravity
• Quantum Theory of Weyl Invariant Scalar-tensor Gravity
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