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The Nakano-Nishijima-Gell-Mann Formula from Discrete Galois Fields
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Title: | The Nakano-Nishijima-Gell-Mann Formula from Discrete Galois Fields |
Authors: | Nakatsugawa, Keiji Browse this author | Ohaga, Motoo Browse this author | Fujii, Toshiyuki Browse this author | Matsuyama, Toyoki Browse this author | Tanda, Satoshi Browse this author →KAKEN DB |
Keywords: | quantum theory | finite mathematics | Nakano-Nishijima-Gell-Mann formula | fractional quantum number | quark confinement |
Issue Date: | Oct-2020 |
Publisher: | MDPI |
Journal Title: | Symmetry |
Volume: | 12 |
Issue: | 10 |
Start Page: | 1603 |
Publisher DOI: | 10.3390/sym12101603 |
Abstract: | The well known Nakano-Nishijima-Gell-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). |
Rights: | https://creativecommons.org/licenses/by/4.0/ |
Type: | article |
URI: | http://hdl.handle.net/2115/79986 |
Appears in Collections: | 工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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