The Nakano–Nishijima–Gell-Mann Formula from Discrete Galois Fields

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).