Gauge conditions in the perturbative quantization of quadratic gravity and its quantum Lagrangian
Abstract
In the perturbative formulation of the Hamiltonian of quadratic gravity, a specific gauge condition is required to hold the equivalence of the Hamiltonian equations of motion with the covariant field equations. Here we give robust evidence that this is an effect of perturbations, the exact nonperturbative equations of both formulations are equivalent, with no need of specific gauge conditions. Despite this, the required gauge condition must be imposed in the perturbative approach. We use it, together with other conditions obtained on very broad grounds, to obtain the quantum Lagrangian resulting from the integration on the canonical variables of the BFV quantization of the theory. This allow us to characterize the quantum modes from the Lagrangian perspective.
Versions
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BibTeX
@misc{bellorin2026gauge,
title = {{Gauge conditions in the perturbative quantization of quadratic gravity and its quantum Lagrangian}},
author = {Jorge Bellorin and Claudio Bórquez and Byron Droguett},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31839},
eprint = {2610.31839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31839},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gauge conditions in the perturbative quantization of quadratic gravity and its quantum Lagrangian
AU - Jorge Bellorin
AU - Claudio Bórquez
AU - Byron Droguett
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31839
UR - https://arxiv.org/abs/2610.31839
AB - In the perturbative formulation of the Hamiltonian of quadratic gravity, a specific gauge condition is required to hold the equivalence of the Hamiltonian equations of motion with the covariant field equations. Here we give robust evidence that this is an effect of perturbations, the exact nonperturbative equations of both formulations are equivalent, with no need of specific gauge conditions. Despite this, the required gauge condition must be imposed in the perturbative approach. We use it, together with other conditions obtained on very broad grounds, to obtain the quantum Lagrangian resulting from the integration on the canonical variables of the BFV quantization of the theory. This allow us to characterize the quantum modes from the Lagrangian perspective.
ER -