BRST Quantization of General Relativity in Unimodular Gauge and Unimodular Gravity

Abstract

Unimodular gravity (UG) is an important theory which may explain the smallness of the cosmological constant. To get insight into the covariant quantization of UG, we discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We develop a novel way to gauge fix the transverse diffeomorphism (TDiff) and then further to fulfill the unimodular gauge. This process requires the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the TDiff. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then study a theory derived by making "Fourier transform" of GR in the unimodular gauge with respect to the cosmological constant as a candidate of "quantum UG." We clarify the difference from GR and point out problems in this theory.

arXiv comment20 pages, v2: a ref. is added, and discussions are elaborated on

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Cited by in corpus (11)

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• Covariant BRST Quantization of Unimodular Gravity I -- Formulation with antisymmetric tensor ghosts --
• Thermodynamics of spacetime and unimodular gravity
• The cosmological constant as a boundary term
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity
• de Sitter Space Decay and Cosmological Constant Relaxation in Unimodular Gravity with Charged Membranes
• Thermodynamics as a tool for (quantum) gravitational dynamics
• The quantum dynamics of Lagrange multipliers
• Unimodular Plebański Gravity
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor
• Covariant BRST Quantization of Unimodular Gravity II -- Formulation with a vector antighost --