Derivation of Gell-Mann-Nishijima formula from the electromagnetic field modes of a hadron

TL;DR

This paper proposes a novel interpretation of the Gell-Mann-Nishijima formula by modeling electromagnetic field modes around hadrons, linking quantum numbers to optical-like modes for better conceptual understanding.

Contribution

It introduces a new visual model connecting electromagnetic field modes to hadron quantum numbers, deriving the Gell-Mann-Nishijima formula from electromagnetic field modes.

Findings

Quantum numbers correspond to electromagnetic field modes.

Electromagnetic modes satisfy the Gell-Mann-Nishijima formula.

Provides a visual analogy for hadron quantum numbers.

Abstract

When an electron probes another elementary particle Q, the wave function of the electron can be separated into two independent parts, the first part represents the electronic motion, the second part represents the electromagnetic field mode around the particle Q. In analogy with optical modes $TEM_{nlm}$ for a laser resonator, when the electromagnetic field around the particle Q forms into a mode, the quantum numbers of the mode satisfy the Gell-Mann-Nishijima formula, these quantum numbers are recognized as the charge number, baryon number and strangeness number. The modes are used as a visual model to understand the abstract baryon number and strangeness number of hadrons.