{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:36:14Z","timestamp":1760142974518,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T00:00:00Z","timestamp":1704931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Estonian Research Council","award":["IUT2-27","TK133"],"award-info":[{"award-number":["IUT2-27","TK133"]}]},{"DOI":"10.13039\/501100000780","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["IUT2-27","TK133"],"award-info":[{"award-number":["IUT2-27","TK133"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We derive the stabiliser group of the four-vector, also known as Wigner\u2019s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel subgroup. In the absence of mass, particle states are disentangled into left- and right-handed chiral states, governed by the maximal solvable subgroups sol2\u00b1 of order two. Induced Lorentz transformations are constructed and applied to general representations of particle states. Finally, in our conclusions, it is argued how the spin-flip contribution might be closely related to the occurrence of nonphysical spin operators.<\/jats:p>","DOI":"10.3390\/sym16010097","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T12:56:33Z","timestamp":1704977793000},"page":"97","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Solvable Algebra for Massless Fermions"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4462-4408","authenticated-orcid":false,"given":"Stefan","family":"Groote","sequence":"first","affiliation":[{"name":"Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rein","family":"Saar","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"B1549","DOI":"10.1103\/PhysRev.133.B1549","article-title":"Degenerate Systems and Mass Singularities","volume":"133","author":"Lee","year":"1964","journal-title":"Phys. Rev."},{"key":"ref_2","first-page":"1151","article-title":"QED O(\u03b13) radiative corrections to the reaction e+e\u2212\u2192\u03c4+\u03c4\u2212 including spin and mass effects","volume":"15","author":"Jadach","year":"1984","journal-title":"Acta Phys. Pol. B"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/BF01552550","article-title":"Hard Bremsstrahlung Amplitudes for e+e\u2212 Collisions With Polarized Beams at LEP\/SLC Energies","volume":"33","author":"Kleiss","year":"1987","journal-title":"Z. Phys. 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Clifford Algebr."},{"key":"ref_19","unstructured":"Choi, T., and Cho, S.Y. (2018). Spin operators and representations of the Poincar\u00e9 group. arXiv."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/97\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:44:59Z","timestamp":1760103899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/97"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,11]]},"references-count":19,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010097"],"URL":"https:\/\/doi.org\/10.3390\/sym16010097","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,1,11]]}}}