BRST Quantization of Unimodular Gravity

Abstract

We study the quantization of two versions of unimodular gravity, namely, fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant utilizing standard path integral approach. We derive the BRST symmetry of effective actions corresponding to several relevant gauge conditions. We observe that for some gauge conditions, the restricted gauge structure may complicate the formulation and effective actions, in particular, if the chosen gauge conditions involve the canonical momentum conjugate to the induced metric on the spatial hypersurface. The BRST symmetry is extended further to the finite field-dependent BRST transformation, in order to establish the mapping between different gauge conditions in each of the two versions of unimodular gravity.

26 pages, minor modification in texts

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• Unimodular Gravity vs General Relativity: A status report
• Unimodular quantum gravity and the cosmological constant
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Can quantum fluctuations differentiate between standard and unimodular gravity?
• Exploring new corners of asymptotically safe unimodular quantum gravity
• Unimodular Gauge in Perturbative Gravity and Supergravity
• Non-minimal Tinges of Unimodular Gravity
• Unimodular gravity and the gauge/gravity duality
• Soft-Collinear Effective Theory: BRST Formulation
• Unimodular Gauge and ADM Gravity Path Integral