Batalin-Fradkin-Vilkovisky Quantization of Quadratic Gravity

TL;DR

This work applies the Batalin-Fradkin-Vilkovisky formalism to quantize the most general quadratic gravity theory, formulated via a Hamiltonian approach with first-class constraints. It builds a BFV path integral using BRST symmetry and a flexible gauge-fixing scheme that accommodates time-derivative conditions, enabling analysis of physical and unphysical degrees of freedom. In the linearized regime, it derives propagators for scalar, vector, and tensor sectors, including negative-norm states, and shows that the mass spectrum matches the Stelle result though distributed differently among fields due to a noncovariant decomposition. The study highlights a mandatory traceless spatial-metric condition for classical equivalence when κ^{-2} ≠ 0 and points to future work on covariant measures and potential cancellations among problematic modes in loop computations.

Abstract

We present the Batalin-Fradkin-Vilkovisky quantization of the quadratic gravity theory, which is the most general theory with terms up to quadratic order in curvature. This approach of quantization is based on the Hamiltonian formulation. In this sense, this study contributes to the consistency of the quantum formulation of the theory. With this scheme of quantization we may introduce a broad class of additional conditions on the field variables, by including Lagrange multipliers and time derivatives. We find that a mandatory condition for the validity of the Hamiltonian formulation, previously known from classical analysis, can be incorporated consistently in this quantization. We obtain the propagators of the fields, including the propagators associated with the quantum states of negative norm. The spectrum of masses coincides with the results of Stelle, but distributed on a different way among the fields.