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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).
Type: article
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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