The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields

TL;DR

This paper derives the Nakano-Nishijima-Gell-Mann formula using discrete Galois fields instead of real numbers, providing a new algebraic foundation that incorporates fundamental invariance laws and explains quark confinement.

Contribution

It introduces a novel derivation of the NNG formula using discrete Galois fields, unifying meson and baryon representations and linking quark confinement to algebraic fractionality.

Findings

Derivation of NNG formula from discrete Galois fields

Unified treatment of meson and baryon representations

Explanation of quark confinement via algebraic fractionality

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 $I_z$ (isospin), $S$ (strangeness), etc., is constructed using group theory with real numbers $\mathbb{R}$. But, using a discrete Galois field $\mathbb{F}_p$ instead of $\mathbb{R}$ 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).