Quantum scale invariant gravity in the de Donder gauge

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 Faddeev-Popov (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 Poincare-like IOSp(8 vertical bar 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.

Automated summary

In this paper, we perform the manifestly covariant quantization of a scale invariant gravity with a scalar field in the de Donder gauge condition. By deriving various equal-time (anti)commutation relations, it is shown that the general action with the de Donder gauge possesses a Poincare-like IOSp(8 vertical bar 8) supersymmetry. The paper also derives the equal-time commutation relations for the gravitational sector involving the metric tensor and scalar fields, and explains how scale symmetry is spontaneously broken in quantum gravity, showing that the dilaton is a massless Nambu-Goldstone particle.