{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:57:18Z","timestamp":1760057838723,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T00:00:00Z","timestamp":1740355200000},"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>As shown by Dyson in his famous paper \u201cMissed Opportunities\u201d, it follows, even from purely mathematical considerations, that quantum Poincare symmetry is a special degenerate case of quantum de Sitter symmetries. Thus, the usual explanation of why, in particle physics, Poincare symmetry works with a very high accuracy is as follows. A theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space is very high. However, the answer to this question must be given only in terms of quantum concepts, while de Sitter and Minkowski spaces are purely classical concepts. Quantum Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators M4\u03bc of the anti-de Sitter algebra are much greater than the eigenvalues of the operators M\u03bc\u03bd (\u03bc,\u03bd=0,1,2,3). We explicitly show that this is the case in the Flato\u2013Fronsdal approach, where elementary particles in standard theory are bound states of two Dirac singletons.<\/jats:p>","DOI":"10.3390\/sym17030338","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T07:46:57Z","timestamp":1740383217000},"page":"338","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Why Poincare Symmetry Is a Good Approximate Symmetry in Particle Theory"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4476-3080","authenticated-orcid":false,"given":"Felix M.","family":"Lev","sequence":"first","affiliation":[{"name":"Independent Researcher, San Diego, CA 92101, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,24]]},"reference":[{"key":"ref_1","unstructured":"Novozhilov, Y.V. (1975). Introduction to Elementary Particle Theory. International Series of Monographs in Natural Philosophy, Elsevier. B01K2IQ5L2 Pergamon."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lev, F.M. (2020). Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory. With Application to Gravity and Particle Theory, Springer.","DOI":"10.1007\/978-3-030-61101-9"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1090\/S0002-9904-1972-12971-9","article-title":"Missed Opportunities","volume":"78","author":"Dyson","year":"1972","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1063\/1.1705183","article-title":"Discrete series for the universal covering group of the 3+2 de Sitter group","volume":"8","author":"Evans","year":"1967","journal-title":"J. Math. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lev, F.M. (2024). Solving Particle\u2013Antiparticle and Cosmological Constant Problems. Axioms, 13.","DOI":"10.3390\/axioms13030138"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/0370-2693(82)91038-3","article-title":"All Linear Unitary Irreducible Representations of de Sitter Supersymmetry with Positive Energy","volume":"110","author":"Heidenreich","year":"1982","journal-title":"Phys. Lett. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1063\/1.1703672","article-title":"Normal Form of Antiunitary Operators","volume":"1","author":"Wigner","year":"1960","journal-title":"J. Math. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1103\/PhysRev.91.713","article-title":"The Theory of Quantized Fields II","volume":"91","author":"Schwinger","year":"1953","journal-title":"Phys. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/BF00400170","article-title":"One Massles Particle Equals two Dirac Singletons","volume":"2","author":"Flato","year":"1978","journal-title":"Lett. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1063\/1.525099","article-title":"Tensor Product of Positive Energy Representations of S\u02dc(3, 2) and S\u02dc(4, 2)","volume":"22","author":"Heidenreich","year":"1981","journal-title":"J. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1063\/1.1704016","article-title":"A Remarkable Representation of the 3 + 2 de Sitter group","volume":"4","author":"Dirac","year":"1963","journal-title":"J. Math. Phys."},{"key":"ref_12","unstructured":"Flato, M., Fronsdal, C., and Sternheimer, D. (1999). Singleton Physics. arXiv."},{"key":"ref_13","unstructured":"Bekaert, X. (2011). Singletons and Their Maximal Symmetry Algebras. arXiv."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bekaert, X., and Oblak, B. (2022). Massless Scalars and Higher-Spin BMS in Any Dimension. arXiv.","DOI":"10.1007\/JHEP11(2022)022"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ponomarev, D. (2022). Towards Higher-spin Holography in Flat Fpace. arXiv.","DOI":"10.1007\/JHEP09(2022)086"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ponomarev, D. (2022). Chiral Higher-spin Holography in Flat Space: The Flato-Fronsdal Theorem and Lower-Point Functions. arXiv.","DOI":"10.1007\/JHEP01(2023)048"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bekaert, X., Campoleoni, A., and Pekar, S. (2022). Carrollian Conformal Scalar as Flat-space Singleton. arXiv.","DOI":"10.1007\/JHEP02(2022)150"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Samtleben, H., and Sezgin, E. (2024). Singletons in Supersymmetric Field Theories and in Supergravity. arXiv.","DOI":"10.1088\/1751-8121\/adb2c6"},{"key":"ref_19","unstructured":"Bohm, D. (1989). Quantum Theory, Dover Publications."},{"key":"ref_20","unstructured":"Landau, L.D., and Lifshits, E.M. (1981). Quantum Mechanics: Non-Relativistic Theory, Butterworth-Heinemann."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/338\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:41:12Z","timestamp":1760028072000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/338"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,24]]},"references-count":20,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030338"],"URL":"https:\/\/doi.org\/10.3390\/sym17030338","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,2,24]]}}}