{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T17:03:28Z","timestamp":1761930208576,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:00:00Z","timestamp":1634083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["109-2119-M-008-016"],"award-info":[{"award-number":["109-2119-M-008-016"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes\u2014via the notion of symmetry contractions\u2014a natural way in which one can understand how the Newtonian theory arises as an approximation to Einstein\u2019s theory. We begin with the Poincar\u00e9 symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group. Then, we proceed to the parallel for the phase space of a spin zero particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation, illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented. While all notions involved are well established, the systematic presentation of that story as one coherent picture fills a gap in the literature on the subject matter.<\/jats:p>","DOI":"10.3390\/sym13101925","type":"journal-article","created":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T21:48:39Z","timestamp":1634161719000},"page":"1925","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3832-648X","authenticated-orcid":false,"given":"Otto C. W.","family":"Kong","sequence":"first","affiliation":[{"name":"Department of Physics and Center for High Energy and High Field Physics, National Central University, Chung-Li 32054, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6545-9945","authenticated-orcid":false,"given":"Jason","family":"Payne","sequence":"additional","affiliation":[{"name":"Department of Physics and Center for High Energy and High Field Physics, National Central University, Chung-Li 32054, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,13]]},"reference":[{"key":"ref_1","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_2","first-page":"104","article-title":"Raum und Zeit, Lecture to the 80th Assembly of Natural Scientists (Koln, 1908)","volume":"10","author":"Minkowski","year":"1909","journal-title":"Phys. Z."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"553","DOI":"10.4236\/jhepgc.2019.53031","article-title":"Observables and Dynamics Quantum to Classical from a Relativity Symmetry and Noncommutative-Geometric Perspective","volume":"5","author":"Chew","year":"2019","journal-title":"J. High Energy Phys. Gravit. Cosmol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bedi\u0107, S., Kong, O.C.W., and Ting, H.K. (2021). Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and c\u2192\u221e Limit. Symmetry, 13.","DOI":"10.3390\/sym13010022"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kong, O.C.W., and Ting, H.K. Quantum Origin of (Newtonian) Particle Mass and Symmetry for Lorentz Covariant Physics. NCU-HEP-k094. Unpublished work, 2021.","DOI":"10.2139\/ssrn.4266951"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"De Azc\u00e1rraga, J.A., and Izquierdo, J.M. (1995). Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics, Cambridge University Press.","DOI":"10.1017\/CBO9780511599897"},{"key":"ref_7","unstructured":"Gilmore, R. (2005). Lie Groups, Lie Algebras, and Some of Their Applications, Dover Publications, Inc."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tung, W.-K. (1985). Group Theory in Physics, World Scientific.","DOI":"10.1142\/0097"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Johns, O.D. (2005). Analytical Mechanics for Relativity and Quantum Mechanics, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780198567264.001.0001"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1073\/pnas.39.6.510","article-title":"On the Contraction of Groups and their Representations","volume":"39","author":"Wigner","year":"1953","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Sudarshan, E.C.G., and Mukunda, N. (2015). Classical Dynamics: A Modern Perspective, World Scientific.","DOI":"10.1142\/9751"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4395918","DOI":"10.1155\/2017\/4395918","article-title":"A Quantum Space Behind Simple Quantum Mechanics","volume":"2017","author":"Chew","year":"2017","journal-title":"Adv. High Energy Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1103\/PhysRev.71.38","article-title":"Quantized Space-Time","volume":"71","author":"Snyder","year":"1947","journal-title":"Phys. Rev."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1063\/1.1664490","article-title":"Possible Kinematics","volume":"9","author":"Bacry","year":"1968","journal-title":"J. Math. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.physletb.2008.05.060","article-title":"A deformed relativity with the quantum \u210f","volume":"665","author":"Kong","year":"2008","journal-title":"Phys. Lett. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0370-2693(01)00506-8","article-title":"Testable Scenario for Relativity with Minimum Length","volume":"510","year":"2001","journal-title":"Phys. Lett. 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Introduction to Mechanics and Symmetry, Springer.","DOI":"10.1007\/978-1-4612-2682-6"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1925\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:12:40Z","timestamp":1760166760000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1925"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,13]]},"references-count":19,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101925"],"URL":"https:\/\/doi.org\/10.3390\/sym13101925","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,10,13]]}}}