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Batalin-Fradkin-Vilkovisky quantization of quadratic gravity

Jorge Bellorin1,*, Claudio Bórquez2,†, and Byron Droguett1,‡

  • *Contact author: jorge.bellorin@uantof.cl
  • †Contact author: claudio.borquez@uss.cl
  • ‡Contact author: byron.droguett@uantof.cl
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Phys. Rev. D 113, 106006 – Published 8 May, 2026

DOI: https://doi.org/10.1103/c22r-2v5h

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 [Renormalization of higher derivative quantum gravity, Phys. Rev. D 16, 953 (1977)], but distributed on a different way among the fields.

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Phys. Rev. D 113, 106006– Published 8 May, 2026
  • Received 30 November 2025
  • Accepted 6 April 2026
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