{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/relativistic-closed-form-hamiltonian-for-many","title":"Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation","arxiv_id":"0807.0214","date":"2008-07-01","proceeding":null,"authors":["Tomas Ledvinka","Gerhard Schaefer","Jiri Bicak"],"abstract":"The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.","url_abs":"http://arxiv.org/abs/0807.0214v1","url_pdf":"http://arxiv.org/pdf/0807.0214v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"relativistic-closed-form-hamiltonian-for-many","repo_url":"https://github.com/justincfeng/PoMiN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}