2024-03-28T22:19:34Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/799862022-11-17T02:08:08Zhdl_2115_20045hdl_2115_139The Nakano-Nishijima-Gell-Mann Formula from Discrete Galois FieldsNakatsugawa, KeijiOhaga, MotooFujii, ToshiyukiMatsuyama, ToyokiTanda, Satoshiquantum theoryfinite mathematicsNakano-Nishijima-Gell-Mann formulafractional quantum numberquark confinement421The 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).MDPIJournal Articlehttp://hdl.handle.net/2115/79986Symmetry121016032020-10enginfo:doi/10.3390/sym12101603none