Diophantine Quantization: Application of the Methods of Algebraic Number Theory to the Theory of Elementary Particles

Abstract

The Gell-Mann---Okubo broken-$\mathrm{SU}(3)$ meson mass formula is treated as a quadratic Diophantine equation and solved in integers. The relative masses of $\ensuremath{\pi}$, $\ensuremath{\eta}$, $K$, many known ${K}^{*}$, and the probable lowest $L$ may be predicted unambiguously. The requirement of least-integer solutions mandates a unit mass of 70 MeV ($137{m}_{e}{c}^{2}$). Connections between rest masses and angular momenta can be made, and there is evidence of a general linear group.