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arXiv · 2510.16543

On Time-Evolution in Quantum Gravity

Lasha Berezhiani·Gia Dvali·Otari Sakhelashvili
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Abstract

We derive an explicit BRST-exact operator identity for the bulk Hamiltonian in quantum gravity, working within a BRST-invariant quantization of General Relativity, treated as a low-energy effective field theory. We show that, up to a boundary term, the Hamiltonian can be written elegantly as the anticommutator of the BRST charge and the temporal ghost field. This form makes manifest that the Hamiltonian flow acts as a time-reparameterization on the correlation functions of the physical degrees of freedom. We demonstrate that the BRST-exactness of the bulk Hamiltonian does not trivialize the time evolution of gravitational backgrounds or bulk correlators, nor does it trivialize scattering amplitudes.

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Lasha Berezhiani, Gia Dvali, Otari Sakhelashvili. 2025-10-18. On Time-Evolution in Quantum Gravity. https://doi.org/10.1016/j.physletb.2026.140768

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