{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T15:49:08Z","timestamp":1782748148875,"version":"3.54.5"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T00:00:00Z","timestamp":1756339200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The graph theory-based approach to the three-body problem is introduced. Vectors of linear and angular momenta of the particles form the vertices of the graph. Scalar products of the vectors of the linear and angular momenta define the colors of the links connecting the vertices. The bi-colored, complete graph emerges. This graph is called the \u201cmomenta graph\u201d. According to the Ramsey theorem, this graph contains at least one mono-chromatic triangle. This is true even for chaotic motion of three bodies; thus, illustrating the idea supplied by the Ramsey theory, total chaos is impossible. Coloring of the graph is independent on the rotation of frames; however, it is sensitive to Galilean transformations. The coloring of the momenta graph remains the same for general linear transformations of vectors with a positive-definite matrix. For a given motion, changing the order of the vertices does not change the number and distribution of monochromatic triangles. Symmetry of the momenta graph is addressed. The symmetry group remains the same for general linear transformation of vectors of the linear and angular momenta with a positive-definite matrix. Conditions defining conservation of the coloring of the momenta graph are addressed. The notion of the stereographic momenta graph is introduced. Shannon entropy of the momenta graph is calculated. The particular configurations of bodies are addressed, including the Lagrange configuration and the figure eight-shaped motion. The suggested approach is generalized for the quantum field theory with the Pauli\u2013Lubanski pseudo-vector. The suggested coloring procedure is the Lorenz invariant.<\/jats:p>","DOI":"10.3390\/sym17091404","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T10:29:18Z","timestamp":1756376958000},"page":"1404","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Three-Body Problem: The Ramsey Approach and Symmetry Considerations in the Classical and Quantum Field Theories"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1356-2486","authenticated-orcid":false,"given":"Edward","family":"Bormashenko","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering, Ariel University, Ariel 407000, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3025-6130","authenticated-orcid":false,"given":"Mark","family":"Frenkel","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, Ariel University, Ariel 407000, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"065901","DOI":"10.1088\/0034-4885\/77\/6\/065901","article-title":"The three-body problem","volume":"77","author":"Musielak","year":"2014","journal-title":"Rep. 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