Canonical Quantum Theory of Gravitational Field with Higher Derivatives

Manifestly Covariant Canonical Formalism of Quantum Gravity - Systematic Presentation of the Theory

“…Kawasaki, Kimura, and Kitago [48], [49] made an extension of our theory to the case in which the Lagrangian density effectively contains the terms proportional to hR^'R^ and to hR 2 (but without ^LGF + ^LFP + ^MF)-After extremely elaborate calculation of equal-time *-commutators, they confirmed that the choral symmetry remains valid at the operator level. The tensorlike com-mutation relation (10.1) was also confirmed in this case.…”

Quantum conformal gravity

“…In order to perform the canonical quantization, it is more convenient to introduce an auxiliary symmetric tensor K µν = K νµ and a Stückelberg-like vector field A µ , 3 and rewrite L CG , which is the Lagrangian of conformal gravity, into a form [6][7][8][9]:…”

“…whereas in the quantum conformal gravity, it turns out that the WS BRST charge has a very complicated nonlinear structure. 6 In this sense, the quantum conformal gravity is similar to QCD rather than the QED. Lastly, let us note that such nonlinear global symmetries cannot be described by the generators of the Poincaré-like IOSp(8|8) symmetry.…”

High-energy properties of the graviton scattering in quadratic gravity

“…Two alternative ways of quantizing higher derivative gravity have been given in the past, the path integral method [11] and the canonical quantization [41]. The latter method seems more suitable for our purpose of computing scattering amplitudes and of dealing with negative norm states.…”

“…In this appendix, we give the canonical quantization for massive graviton I µν . The canonical quantization for graviton is given in [42,43] for the massless graviton, in [44] for the massive graviton, in [41] for the quadratic gravity and in [54] for the conformal gravity. Some of them involve the Faddeev-Popov ghosts in addition to the gauge fixing terms.…”