Quantum Gravity Study Derives BRST-Exact Hamiltonian, Preserving Time Evolution of Gravitational Backgrounds

High Energy Physics - Theory arXiv:2510.16543 (hep-th) [Submitted on 18 Oct 2025] Title:On Time-Evolution in Quantum Gravity Authors:Lasha Berezhiani, Gia Dvali, Otari Sakhelashvili View a PDF of the paper titled On Time-Evolution in Quantum Gravity, by Lasha Berezhiani and 1 other authors View PDF HTML (experimental) 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. Comments: Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph) Cite as: arXiv:2510.16543 [hep-th] (or arXiv:2510.16543v1 [hep-th] for this version) https://doi.org/10.48550/arXiv.2510.16543 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Otari Sakhelashvili [view email] [v1] Sat, 18 Oct 2025 15:38:28 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled On Time-Evolution in Quantum Gravity, by Lasha Berezhiani and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: hep-th new | recent | 2025-10 Change to browse by: gr-qc math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)