{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:16:59Z","timestamp":1760239019483,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,9,26]],"date-time":"2020-09-26T00:00:00Z","timestamp":1601078400000},"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 well known Nakano\u2013Nishijima\u2013Gell-Mann (NNG) formula relates certain quantum numbers of elementary particles to their charge number. This equation, which phenomenologically introduces the quantum numbers Iz (isospin), S (strangeness), etc., is constructed using group theory with real numbers R. But, using a discrete Galois field Fp instead of R and assuring the fundamental invariance laws such as unitarity, Lorentz invariance, and gauge invariance, we derive the NNG formula deductively from Meson (two quarks) and Baryon (three quarks) representations in a unified way. Moreover, we show that quark confinement ascribes to the inevitable fractionality caused by coprimeness between half-integer (1\/2) of isospin and number of composite particles (e.g., three).<\/jats:p>","DOI":"10.3390\/sym12101603","type":"journal-article","created":{"date-parts":[[2020,9,28]],"date-time":"2020-09-28T10:39:58Z","timestamp":1601289598000},"page":"1603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Nakano\u2013Nishijima\u2013Gell-Mann Formula from Discrete Galois Fields"],"prefix":"10.3390","volume":"12","author":[{"given":"Keiji","family":"Nakatsugawa","sequence":"first","affiliation":[{"name":"Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan"},{"name":"Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo 060-8628, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Motoo","family":"Ohaga","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan"},{"name":"Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo 060-8628, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toshiyuki","family":"Fujii","sequence":"additional","affiliation":[{"name":"Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo 060-8628, Japan"},{"name":"Department of Physics, Asahikawa Medical University, Asahikawa 078-8510, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toyoki","family":"Matsuyama","sequence":"additional","affiliation":[{"name":"Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo 060-8628, Japan"},{"name":"Department of Physics, Nara University of Education, Takabatake-cho, Nara 630-8528, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Satoshi","family":"Tanda","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan"},{"name":"Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo 060-8628, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1143\/PTPS.37.512","article-title":"Atomistics and the Divisibility of Space and Time","volume":"37\u201338","author":"Yukawa","year":"1966","journal-title":"Prog. 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