离散Galois域上的Nakano-Nishijima-Gell-Mann公式
The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields
摘要：
众所周知的Nakano-Nishijima-Gell-Mann（NNG）公式将基本粒子的某些量子数与它们的电荷数联系起来。这个方程唯象地引入了量子数$I_z$（同位旋）、$S$（奇异性）等，是使用实数$\mathbb{R}$的群论构造的。但是，我们用离散的伽罗瓦场$\mathbb{F}_p$代替$\mathbb{R}$，在保证幺正性、洛伦兹不变性和规范不变性等基本不变性定律的前提下，统一地从介子（两夸克）和重子（三夸克）表示演绎导出了NNG公式。此外，我们发现夸克禁闭归因于不可避免的分数所造成的半整数（1/2）的同位旋和复合粒子的数量（如3）之间的互质性。
英文摘要：
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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
